Finite Group Databasebeta

← Group #13172153

Character table — Group #13172153

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666623336666666666644366666666666666622444661212121212124466666661212121212121212121212121224444661212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-111111-1-111-1-11-1-111-1-111-111111111-1-1-11-1-11-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-111-1-1111111-1-1-111-1-1111-111-11111-1-1111-11-1-111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-11-1-11-11111-1-1-1-1-1-1-11-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-111111111111111111111-111-1-111-1-1111111111-111-11-1-1-1-11111-1-1-11-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-111-1-1-1-1-1-1-1-11-1-111-1-1-11-1-11-1-1-1-111-1-11-11-1-111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-11-1-1-1-1-111-1-1-1-1-111-1-111-1-11-1-1-1-1-1-1-1-111-11-1-11-1-111-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111-1-111-1-11111111-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-111
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-111111111111-1-111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-1-11111-1-1-1
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-111-1-11111-111-1-111-11-1-1111-1-111-1-1-1-11-11-1-1-1-1-1-1111111-1
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1111-1-111111-1-11111-1-111-1-1-1-11-11
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111111-1-11-1-1-111-1-1-1-11-1-11111-1-111-1-1111-1-1
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-111-1-1111-1-111-1-11-111-1-1-111-1-111-1-11-11-1-1-1-1-1-111-1-1111
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-1-1-1-1-1-111-111-1-11111-111-1-11111-1-111-1-1-11111-1-111-1-1-1-11
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1111-1-1-11111-1-111-11-1
χ17222222-12-122-12-1222-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10202200-1-1-1-1220002-100-1-1202-10-1-1-1-100-1-120200-1-1000000000-10
χ18222222-12-122-12-1222-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2200-1-11122000-21001120-2-10-1-1-1-10011-20-2001100000000010
χ19222222-12-122-12-1222-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10202-20011-1-1-2-20002-100-1-1-20210111100-1-1-20-2001100000000010
χ20222222-12-122-12-1222-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2-2001111-2-2000-210011-20-2101111001120200-1-1000000000-10
χ21222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-11111020-2-200-1-111220002-100-1-1-20-210-1-1110011-2020011000000000-10
χ22222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-111110-202-200-1-1-1-122000-210011-20210-1-11100-1-120-200-1-100000000010
χ23222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-11111020-22001111-2-20002-100-1-120-2-1011-1-1001120-200-1-100000000010
χ24222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110-20220011-1-1-2-2000-210011202-1011-1-100-1-1-2020011000000000-10
χ2522222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1222202200220022-1-12-1-1-1-10-1-1020000-1-1-1-1000200000-1-1-1-100000
χ2622222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-22-202200-2-200-2-2-11-2-1-1110-11020000-1-111000-200000111100000
χ2722222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-22-220-2-2002200-2-21-1211-1-101-10-2000011-1-1000-200000111100000
χ2822222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-200-2-2002211-211110110-200001111000200000-1-1-1-100000
χ2922222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-1111122-2-202200-2-200-2-2-1-12-1-1-1-10110-200001111000200000-1-11100000
χ3022222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-111112-2-2202200220022-11-2-1-11101-10-2000011-1-1000-20000011-1-100000
χ3122222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-222-20-2-200-2-200221-1211-1-10-11020000-1-111000-20000011-1-100000
χ3222222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2-2220-2-2002200-2-211-211110-1-1020000-1-1-1-1000200000-1-11100000
χ332222-12222-122-12-122-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-120202-1-12200-1-100200-1-100-1202-1-1-1-1-1-1-1000200200-1-1000000-100
χ342222-12222-122-12-122-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1-20-202112200-1-100-2001100-1-2021-1-1-1-111000-200-20011000000100
χ352222-12222-122-12-122-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-12020-2-1-1-2-2001100200-1-100120-2-11111-1-1000-200-20011000000100
χ362222-12222-122-12-122-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-20-211-2-2001100-20011001-20-21111111000200200-1-1000000-100
χ372222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-1111120-20-2-1-12200-1-100200-1-1001-20-21-1-11111000200-200-1-1000000100
χ382222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-11111-2020-2112200-1-100-2001100120-2-1-1-111-1-1000-20020011000000-100
χ392222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-1111120-202-1-1-2-2001100200-1-100-1-202111-1-111000-20020011000000-100
χ402222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111-2020211-2-2001100-2001100-1202-111-1-1-1-1000200-200-1-1000000100
χ412-2-2222222-2-2-22-2-2-202220022-22-2-2-2-2-22i−2i2000000002-2-2000000000002i−2i002i−2i2i−2i0000000000002i−2i000000000000000002i−2i2-2000
χ422-2-2222222-2-2-22-2-2-202220022-22-2-2-2-2-22i−2i2000000002-2-2000000000002i−2i002i−2i−2i2i0000000000002i−2i00000000000000000−2i2i-22000
χ432-2-2222222-2-2-22-2-2-202220022-22-2-2-2-2-2−2i2i2000000002-2-200000000000−2i2i00−2i2i2i−2i000000000000−2i2i000000000000000002i−2i-22000
χ442-2-2222222-2-2-22-2-2-202220022-22-2-2-2-2-2−2i2i2000000002-2-200000000000−2i2i00−2i2i−2i2i000000000000−2i2i00000000000000000−2i2i2-2000
χ4544444-2-2-2-24-2-24-24-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-2111111111040400000-2-200000-2-2001100-20000000011000000000000000000
χ4644444-2-2-2-24-2-24-24-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110-40-40000022000002200-1-100200000000-1-1000000000000000000
χ4744444-2-2-2-24-2-24-24-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-1040-4000002200000-2-2001100200000000-1-1000000000000000000
χ4844444-2-2-2-24-2-24-24-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10-40400000-2-2000002200-1-100-20000000011000000000000000000
χ494444-24-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-2441-2-211-2-2-2-211111110000400-2-200-2-2000000000-200-2011110000000000000000000000
χ504444-24-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-2-4-41-2-211-2-2-2-211111110000-40022002200000000020020-1-1-1-10000000000000000000000
χ514444-24-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-244122-1-12222111-1-1-1-10000-400-2-200-2-20000000002002011-1-10000000000000000000000
χ524444-24-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2-4-4122-1-12222111-1-1-1-10000400220022000000000-200-20-1-1110000000000000000000000
χ534444-2-24-24-2-24-24-2-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-2111111140400-2-200000000-20011000-200-200001100000000000000000000
χ544444-2-24-24-2-24-24-2-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-21111111-40-4002200000000200-1-100020020000-1-100000000000000000000
χ554444-2-24-24-2-24-24-2-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-140-400-2-200000000-2001100020020000-1-100000000000000000000
χ564444-2-24-24-2-24-24-2-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-1-404002200000000200-1-1000-200-200001100000000000000000000
χ5744-4-4444-4-4-444-4-44-4044400-4-4-4-4-44-44400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-42-44-2-424-40-24-2002-4-422-224-200-2000000002-220000000000000−2i32i30000000000000000000000−2i32i3000000000000000000
χ5944-4-444-2-42-44-2-424-40-24-2002-4-422-224-200-2000000002-2200000000000002i3−2i300000000000000000000002i3−2i3000000000000000000
χ6044-4-44-242-4-4-24-4-44204-2-2−2i32i3-422224-4-2-200-20000−2i32i3−2i32i32-22−2i3−2i32i32i300000000000000000000000000000000000000000000000000000
χ6144-4-44-242-4-4-24-4-44204-2-22i3−2i3-422224-4-2-200-200002i3−2i32i3−2i32-222i32i3−2i3−2i300000000000000000000000000000000000000000000000000000
χ6244-4-44-2-222-4-2-2-42420-2-21−2i32i3222-1-1-22-210010000−2i32i3i3−i3-11-1i3i3−i3−i3000000000−2i32i30000000003-300000000000i3−i3000000000000000000
χ6344-4-44-2-222-4-2-2-42420-2-21−2i32i3222-1-1-22-210010000−2i32i3i3−i3-11-1i3i3−i3−i30000000002i3−2i3000000000-3300000000000−i3i3000000000000000000
χ6444-4-44-2-222-4-2-2-42420-2-212i3−2i3222-1-1-22-2100100002i3−2i3−i3i3-11-1−i3−i3i3i3000000000−2i32i3000000000-3300000000000i3−i3000000000000000000
χ6544-4-44-2-222-4-2-2-42420-2-212i3−2i3222-1-1-22-2100100002i3−2i3−i3i3-11-1−i3−i3i3i30000000002i3−2i30000000003-300000000000−i3i3000000000000000000
χ6644-4-4-244-4-42442-4-2-40-2-2400222-4-4-22-2400-2000000002-22000000000−2i32i300000000000−2i32i3000000000000000000000000000000000
χ6744-4-4-244-4-42442-4-2-40-2-2400222-4-4-22-2400-2000000002-220000000002i3−2i3000000000002i3−2i3000000000000000000000000000000000
χ6844-4-4-2-242-42-242-4-220-21-2−2i32i32-1-122-221-20010000i3−i3−2i32i3-11-1i3i3−i3−i300000−2i32i300000000000i3−i3000000000003-300000000000000000000
χ6944-4-4-2-242-42-242-4-220-21-2−2i32i32-1-122-221-20010000i3−i3−2i32i3-11-1i3i3−i3−i3000002i3−2i300000000000−i3i300000000000-3300000000000000000000
χ7044-4-4-2-242-42-242-4-220-21-22i3−2i32-1-122-221-20010000−i3i32i3−2i3-11-1−i3−i3i3i300000−2i32i300000000000i3−i300000000000-3300000000000000000000
χ7144-4-4-2-242-42-242-4-220-21-22i3−2i32-1-122-221-20010000−i3i32i3−2i3-11-1−i3−i3i3i3000002i3−2i300000000000−i3i3000000000003-300000000000000000000
χ724-44-4444-4-44-4-4-44-44044400-4-44-44-44-4-400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ734-44-444-2-424-42-4-2-440-24-2002-442-22-2-4200-20000000022-200000000000000000000000000000000000000000000−2i32i300000000000
χ744-44-444-2-424-42-4-2-440-24-2002-442-22-2-4200-20000000022-2000000000000000000000000000000000000000000002i3−2i300000000000
χ754-44-44-242-442-4-44-4-204-2-200-42-22-2-442200-20000000022-2000000000000000000000000000000000000000000000000−2i32i30000000
χ764-44-44-242-442-4-44-4-204-2-200-42-22-2-442200-20000000022-20000000000000000000000000000000000000000000000002i3−2i30000000
χ774-44-4-244-4-4-2-4-424240-2-240022-2-442-22-400-20000000022-2000000000000000000000000000000000000000000000023−23000000000
χ784-44-4-244-4-4-2-4-424240-2-240022-2-442-22-400-20000000022-20000000000000000000000000000000000000000000000−2323000000000
χ794-4-4444-24-2-4-4242-4-40-24-200-24-4-2222-424i−4i-200000000-22200000000000−2i2i004i−4i00000000000000−2i2i000000000000000000000000
χ804-4-4444-24-2-4-4242-4-40-24-200-24-4-2222-42−4i4i-200000000-222000000000002i−2i00−4i4i000000000000002i−2i000000000000000000000000
χ814-4-444-24-24-42-44-4-4204-2-2004-22-22-4-42200-200000000-222000000000000000004i−4i0000000000000000000000000000000−2i2i00000
χ824-4-444-24-24-42-44-4-4204-2-2004-22-22-4-42200-200000000-22200000000000000000−4i4i00000000000000000000000000000002i−2i00000
χ834-4-44-244442-4-4-2-42-40-2-2400-2-224-4222-44i−4i-200000000-222000000000004i−4i00−2i2i00000000000000−2i2i000000000000000000000000
χ844-4-44-244442-4-4-2-42-40-2-2400-2-224-4222-4−4i4i-200000000-22200000000000−4i4i002i−2i000000000000002i−2i000000000000000000000000
χ854-4-44-24-24-22-42-222-401-2-2001-22-22-1-1224i−4i1003-300001-1-13-33-30000000−2i2i00−2i2i00000000000000i−i3i−3i0000000000000000000000
χ864-4-44-24-24-22-42-222-401-2-2001-22-22-1-1224i−4i100-3300001-1-1-33-330000000−2i2i00−2i2i00000000000000i−i−3i3i0000000000000000000000
χ874-4-44-24-24-22-42-222-401-2-2001-22-22-1-122−4i4i1003-300001-1-13-33-300000002i−2i002i−2i00000000000000−ii−3i3i0000000000000000000000
χ884-4-44-24-24-22-42-222-401-2-2001-22-22-1-122−4i4i100-3300001-1-1-33-3300000002i−2i002i−2i00000000000000−ii3i−3i0000000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-422222222200-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-82224422222222200-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4-8448-444-4-802-4-400-244442-2-4-400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4444-4-444-440222−4i34i3-2-2-2-2-22-22200-100002i3−2i32i3−2i31-11−i3−i3i3i300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4444-4-444-4402224i3−4i3-2-2-2-2-22-22200-10000−2i32i3−2i32i31-11i3i3−i3−i300000000000000000000000000000000000000000000000000000
χ948-88-88-4-444844-8-4-8-40-4-420044-4-224-44-200200000000-2-22000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4-84-4-844-44802-4-400-24-44-4-224400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-8-44-8484-40-42-4004-224-44-4-2400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444-4444-44-4022200-2-22-22-22-2-200-10000000011-1−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444-4444-44-4022200-2-22-22-22-2-200-10000000011-13i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-4-4-84484-840-4-4200-4-442-2444-2002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-4844-8-4-8440-42-400-42-2-4444-24002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-4-4444-444402220022-22-2-2-2-2-200-1006-60000-111-33-3300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-4-4444-444402220022-22-2-2-2-2-200-100-660000-1113-33-300000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).