Finite Group Databasebeta

← Group #13172098

Character table — Group #13172098

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666662333666666666664436666666666666662244466661212121244666666121212121212121212121212121222444121212121212121244664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-111-1-11111-1-11-111-1-11111-1-1111111-1-11-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-11-1-1111111-1-1-11-1-11111-1-1111111-1-111-11-1-11-1-111-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-1111111-1-1-1-111111111-1-11111-1-1-1-11111-1-11-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1-111-1-1-11-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-111-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1111-1-11-111-1-1-1-1-1-1111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111-1-11111-1-11-111-1-1-1-1-1-11111-1-1-1-111-1111-111-1-1-1-111-1-1-111
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1111111-1-1-11-1-111-1-111-1-111-1-111-1-11-11-11-1-111-1-111-1-11-11
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-111-1-11111-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-111-1-1111-11-11-1-111-1-111111-1-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-11-1-1111111-1-1-1-11111-1-1-1111-111-1-1-1-11111-11-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1111111-1-1-111111111-1-1-1-1-1-11
χ17222222-122-122-12-122-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10220200-1-122-1-1000200-1-12-1002-1-1-1-1-100-1-10200200-1-10000000-10
χ18222222-122-122-12-122-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10-220-2001122-1-1000-200112-100-21-1-1-1-100110-200-20011000000010
χ19222222-122-122-12-122-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-102-20200-1-1-2-211000200-1-1-21002-1111100-1-10-200-20011000000010
χ20222222-122-122-12-122-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10-2-20-20011-2-211000-20011-2100-21111100110200200-1-10000000-10
χ21222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-1111102-20-200-1-122-1-1000200-1-1-2100-21-1-11100110-200200-1-1000000010
χ22222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-111110-2-202001122-1-1000-20011-21002-1-1-11100-1-10200-200110000000-10
χ23222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110220-200-1-1-2-211000200-1-12-100-2111-1-100110200-200110000000-10
χ24222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110-22020011-2-211000-200112-1002-111-1-100-1-10-200200-1-1000000010
χ2522222-122-122-12-1222-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-120220-1-100-1-1220020-1-100-122-100-1-1-1-1-1-10020020-1-100000000-100
χ2622222-122-122-12-1222-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1-202-201100-1-12200-201100-12-2100-1-1-1-11100-200-201100000000100
χ2722222-122-122-12-1222-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-120-220-1-10011-2-20020-1-1001-22-1001111-1-100-200-201100000000100
χ2822222-122-122-12-1222-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-20110011-2-200-2011001-2-21001111110020020-1-100000000-100
χ2922222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-1111120-2-20-1-100-1-1220020-1-1001-2-2100-1-1111100-20020-1-100000000100
χ3022222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-11111-20-2201100-1-12200-2011001-22-100-1-111-1-100200-201100000000-100
χ3122222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111202-20-1-10011-2-20020-1-100-12-210011-1-11100200-201100000000-100
χ3222222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111-20220110011-2-200-201100-122-10011-1-1-1-100-20020-1-100000000100
χ332222-122-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1220222222000022-1-1-1-1-1-100-12-120000-1-1-1-1002000000-1-1-1-100000
χ342222-122-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-202-222-2-20000-2-2-11-1-11100-121-20000-1-11100-2000000111100000
χ352222-122-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-220-22-2-2220000-2-21-111-1-1001-2-12000011-1-100-2000000111100000
χ362222-122-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2-2000022111111001-21-200001111002000000-1-1-1-100000
χ372222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111220-2-22222000022-1-1-1-1-1-1001-21-20000111100-2000000-1-11100000
χ382222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-111112-20-2222-2-20000-2-2-11-1-111001-2-12000011-1-100200000011-1-100000
χ392222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2202-2-2-2220000-2-21-111-1-100-121-20000-1-11100200000011-1-100000
χ402222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2-2022-2-2-2-200002211111100-12-120000-1-1-1-100-2000000-1-11100000
χ4122-2-2222-222-2-2-2-2-2202220022-22-2-2-2-2-22i−2i2000000002-2-200000000000002i−2i2i−2i2-20000000000002i−2i0000000000000002-2002i−2i000
χ4222-2-2222-222-2-2-2-2-2202220022-22-2-2-2-2-22i−2i2000000002-2-200000000000002i−2i2i−2i-220000000000002i−2i000000000000000-2200−2i2i000
χ4322-2-2222-222-2-2-2-2-2202220022-22-2-2-2-2-2−2i2i2000000002-2-20000000000000−2i2i−2i2i2-2000000000000−2i2i0000000000000002-200−2i2i000
χ4422-2-2222-222-2-2-2-2-2202220022-22-2-2-2-2-2−2i2i2000000002-2-20000000000000−2i2i−2i2i-22000000000000−2i2i000000000000000-22002i−2i000
χ4544444-2-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-2441-2-211-2-2-2-21111111004000000-2-2-2-200000000-2-2000011110000000000000000000000
χ4644444-2-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-2-4-41-2-211-2-2-2-2111111100-4000000222200000000220000-1-1-1-10000000000000000000000
χ4744444-2-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-244122-1-12222111-1-1-1-100-4000000-2-2-2-20000000022000011-1-10000000000000000000000
χ4844444-2-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2-4-4122-1-12222111-1-1-1-1004000000222200000000-2-20000-1-1110000000000000000000000
χ494444-24-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110400400-2-20000000-200110000-2-200000011000000000000000000
χ504444-24-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110-400-400220000000200-1-1000022000000-1-1000000000000000000
χ514444-24-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10400-400-2-20000000-20011000022000000-1-1000000000000000000
χ524444-24-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10-400400220000000200-1-10000-2-200000011000000000000000000
χ534444-2-24-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-2111111140040-2-200000000-20110000-2-20000001100000000000000000000
χ544444-2-24-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-21111111-400-40220000000020-1-1000022000000-1-100000000000000000000
χ554444-2-24-2-24-2-24-24-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-1400-40-2-200000000-2011000022000000-1-100000000000000000000
χ564444-2-24-2-24-2-24-24-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-1-40040220000000020-1-10000-2-20000001100000000000000000000
χ5744-4-444-2-44-2-4-42-4240-24-200-24-4-2222-424i−4i-200000000-22200000000000004i−4i−2i2i00000000000000−2i2i000000000000000000000000
χ5844-4-444-2-44-2-4-42-4240-24-200-24-4-2222-42−4i4i-200000000-2220000000000000−4i4i2i−2i000000000000002i−2i000000000000000000000000
χ5944-4-44-24-4-24-42-42-440-2-2400-2-224-4222-44i−4i-200000000-2220000000000000−2i2i4i−4i00000000000000−2i2i000000000000000000000000
χ6044-4-44-24-4-24-42-42-440-2-2400-2-224-4222-4−4i4i-200000000-22200000000000002i−2i−4i4i000000000000002i−2i000000000000000000000000
χ6144-4-44-2-2-4-2-2-42222401-2-2001-22-22-1-1224i−4i1003-300001-1-133-3-3000000000−2i2i−2i2i00000000000000i−i3i−3i0000000000000000000000
χ6244-4-44-2-2-4-2-2-42222401-2-2001-22-22-1-1224i−4i100-3300001-1-1-3-333000000000−2i2i−2i2i00000000000000i−i−3i3i0000000000000000000000
χ6344-4-44-2-2-4-2-2-42222401-2-2001-22-22-1-122−4i4i1003-300001-1-133-3-30000000002i−2i2i−2i00000000000000−ii−3i3i0000000000000000000000
χ6444-4-44-2-2-4-2-2-42222401-2-2001-22-22-1-122−4i4i100-3300001-1-1-3-3330000000002i−2i2i−2i00000000000000−ii3i−3i0000000000000000000000
χ6544-4-4-2442442-4-4-4-4-204-2-2004-22-22-4-42200-200000000-222000000000000000004-400000000000000000000000000000-220000000
χ6644-4-4-2442442-4-4-4-4-204-2-2004-22-22-4-42200-200000000-22200000000000000000-44000000000000000000000000000002-20000000
χ674-44-4444-4-4-4444-4-4-4044400-4-4-4-4-44-44400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-4-4244-2-42-40-24-2002-4-422-224-200-2000000002-2200000000000−2i32i30000000000−2i32i300000000000000000000000000000000
χ694-44-444-2-4-4244-2-42-40-24-2002-4-422-224-200-2000000002-22000000000002i3−2i300000000002i3−2i300000000000000000000000000000000
χ704-44-44-24-42-44-242-4-40-2-2400222-4-4-22-2400-2000000002-22000000000−2i32i30000000000−2i32i30000000000000000000000000000000000
χ714-44-44-24-42-44-242-4-40-2-2400222-4-4-22-2400-2000000002-220000000002i3−2i300000000002i3−2i30000000000000000000000000000000000
χ724-44-4-2442-4-4-244-4-4204-2-2−2i32i3-422224-4-2-200-20000−2i32i3−2i32i32-22−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ734-44-4-2442-4-4-244-4-4204-2-22i3−2i3-422224-4-2-200-200002i3−2i32i3−2i32-222i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ744-44-4-24-22-42-24-2-4220-2-21−2i32i3222-1-1-22-210010000−2i32i3i3−i3-11-1i3−i3i3−i30000000−2i32i30000000000i3−i30000000000003-3000000000000000000
χ754-44-4-24-22-42-24-2-4220-2-21−2i32i3222-1-1-22-210010000−2i32i3i3−i3-11-1i3−i3i3−i300000002i3−2i30000000000−i3i3000000000000-33000000000000000000
χ764-44-4-24-22-42-24-2-4220-2-212i3−2i3222-1-1-22-2100100002i3−2i3−i3i3-11-1−i3i3−i3i30000000−2i32i30000000000i3−i3000000000000-33000000000000000000
χ774-44-4-24-22-42-24-2-4220-2-212i3−2i3222-1-1-22-2100100002i3−2i3−i3i3-11-1−i3i3−i3i300000002i3−2i30000000000−i3i30000000000003-3000000000000000000
χ784-44-4-2-2422-4-2-242-420-21-2−2i32i32-1-122-221-20010000i3−i3−2i32i3-11-1i3−i3i3−i300000−2i32i30000000000i3−i30000000000003-300000000000000000000
χ794-44-4-2-2422-4-2-242-420-21-2−2i32i32-1-122-221-20010000i3−i3−2i32i3-11-1i3−i3i3−i3000002i3−2i30000000000−i3i3000000000000-3300000000000000000000
χ804-44-4-2-2422-4-2-242-420-21-22i3−2i32-1-122-221-20010000−i3i32i3−2i3-11-1−i3i3−i3i300000−2i32i30000000000i3−i3000000000000-3300000000000000000000
χ814-44-4-2-2422-4-2-242-420-21-22i3−2i32-1-122-221-20010000−i3i32i3−2i3-11-1−i3i3−i3i3000002i3−2i30000000000−i3i30000000000003-300000000000000000000
χ824-4-444444-4-4-4-4-444-4044400-4-44-44-44-4-400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ834-4-4444-24-42-4-424-2-40-24-2002-442-22-2-4200-20000000022-20000000000000000000000000000000000000000000000−2i32i3000000000
χ844-4-4444-24-42-4-424-2-40-24-2002-442-22-2-4200-20000000022-200000000000000000000000000000000000000000000002i3−2i3000000000
χ854-4-444-2442-4-42-4-24-40-2-240022-2-442-22-400-20000000022-200000000000000000000000000000000000000000000−2i32i300000000000
χ864-4-444-2442-4-42-4-24-40-2-240022-2-442-22-400-20000000022-2000000000000000000000000000000000000000000002i3−2i300000000000
χ874-4-44-244-2-4-42-4-444204-2-200-42-22-2-442200-20000000022-20000000000000000000000000000000000000000000000000023−2300000
χ884-4-44-244-2-4-42-4-444204-2-200-42-22-2-442200-20000000022-200000000000000000000000000000000000000000000000000−232300000
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
χ9188-8-8-48-448-44-84-84-40-4-4200-4-442-2444-2002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-484-4844-84-8-40-42-400-42-2-4444-24002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-444444-402220022-22-2-2-2-2-200-1006-60000-111-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-444444-402220022-22-2-2-2-2-200-100-660000-11133-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-8448-4-444-802-4-400-244442-2-4-400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4444-4-4-44440222−4i34i3-2-2-2-2-22-22200-100002i3−2i32i3−2i31-11−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444-4-4-444402224i3−4i3-2-2-2-2-22-22200-10000−2i32i3−2i32i31-11i3−i3i3−i300000000000000000000000000000000000000000000000000000
χ988-8-888-4-4844-844-4-4-802-4-400-24-44-4-224400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-4-844-848-440-4-420044-4-224-44-200200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-44-844-8-4840-42-4004-224-44-4-2400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-444444-4-44022200-2-22-22-22-2-200-10000000011-1−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-444444-4-44022200-2-22-22-22-2-200-10000000011-13i3−3i3−3i33i300000000000000000000000000000000000000000000000000000

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