Finite Group Databasebeta

← Group #13172205

Character table — Group #13172205

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666233366666666666443666666666666666244441212121212121212226666121212121212121212121212121212122244466666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-11111-1-111-1-111111-1-111-1111111-1-1-1-11-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-1111-1-11111-1-1-1-1-1-1-1111111111-1-11111-1-11-11-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-11-1-1-1-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-11111-1-1111111111-1-11-1-1-1-1111111-11-1-1-1-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-111111-1-11-111-1-1-1-1-1-1111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-111-1-1-1-111111111-11-1-1-1111-1-1-1-111-1-1-1-1-111-1-111-1-1-1-11111-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111-1-11111-1-11111-1-11-1-1-111-1-1-1-1-1-111-1111-1-1-1-1-11111-1-11-11
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-11111-1-111-1-1-1-1-1-111-1-1-1111-1-11111-1-111-1-1111-1-111-1-1-1-1-111
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111111111-1-1-1-11-11-1-1-111-1-111-1-1111-11-1-11111-1-11111-1-1-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-11-1111-1-111-1-111-1-11-11-1-11111-1-111-1-1-1-11
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-1-111-1-1-1-11111-1-1111-1-1-111-1-1-1-11111-1-1111-1-111-1-111-11-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-1-1-1111-1-1-1-1-11111111-1-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-11111-1-111-1-1-1-11-1111-1-1-11111-1-111-1-1-111-1-111-1-1-1-1-1-1111
χ17222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12202200222200222-1-1-1-1-1-10020000-1-1-1-1-1-10200000-1-1-1-10000000
χ18222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-202-20022-2-200-2-22-1-1-1-11100-20000-1-111110-20000011110000000
χ19222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-220-2200-2-22200-2-2-21111-1-1002000011-1-1-1-10-20000011110000000
χ20222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-20-2-200-2-2-2-20022-211111100-200001111110200000-1-1-1-10000000
χ21222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111220-2-200-2-2-2-200222-1-1-11-11002000011-1-1110-200000-1-1110000000
χ22222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-111112-20-2200-2-22200-2-22-1-1-111-100-200001111-1-1020000011-1-10000000
χ23222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2202-20022-2-200-2-2-2111-1-110020000-1-1-1-111020000011-1-10000000
χ24222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2-20220022220022-2111-11-100-20000-1-111-1-10-200000-1-1110000000
χ2522222-12-12222-122-12-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-120220-1-1-1-1002200-12-1-12002-10-1-1-1-1-1-1000020020-1-100000000-100
χ2622222-12-12222-122-12-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-1-202-20-1-1110022001-211-2002-10-1-1-1-1110000-200-201100000000100
χ2722222-12-12222-122-12-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-120-22011-1-100-2-200-12-1-1200-2101111-1-10000-200-201100000000100
χ2822222-12-12222-122-12-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-20-2-20111100-2-2001-211-200-210111111000020020-1-100000000-100
χ2922222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-1111120-2-20-1-111002200-12-1-1-200-210-1-111110000-200201100000000-100
χ3022222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-11111-20-220-1-1-1-10022001-211200-210-1-111-1-10000200-20-1-100000000100
χ3122222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-11111202-20111100-2-200-12-1-1-2002-1011-1-1110000200-20-1-100000000100
χ3222222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-11111-2022011-1-100-2-2001-2112002-1011-1-1-1-10000-200201100000000-100
χ332222-1222222-12-1-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1022022200-1-1-1-1000000022-12-1-1-1-1-100-1-1-1-100202000000-1-1000-10
χ342222-1222222-12-1-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-10-220-2220011-1-10000000-2-2-121-1-1-1-100111100-20-20000001100010
χ352222-1222222-12-1-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-102-202-2-200-1-1110000000221-2-1111100-1-1-1-100-20-20000001100010
χ362222-1222222-12-1-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-2-20-2-2-20011110000000-2-21-21111100111100202000000-1-1000-10
χ372222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-1111102-20-2220011-1-100000002-21-2-1-1-11100-1-11100-20200000011000-10
χ382222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-2-2022200-1-1-1-10000000-221-21-1-1110011-1-10020-2000000-1-100010
χ392222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110220-2-2-200111100000002-2-12-111-1-100-1-1110020-2000000-1-100010
χ402222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110-2202-2-200-1-1110000000-22-12111-1-10011-1-100-20200000011000-10
χ4122-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-22i−2i2000000002-2-20000000002i−2i00002i−2i2-200000000002i−2i0000000000000002-200002i−2i000
χ4222-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-22i−2i2000000002-2-20000000002i−2i00002i−2i-2200000000002i−2i000000000000000-220000−2i2i000
χ4322-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-2000000000−2i2i0000−2i2i2-20000000000−2i2i0000000000000002-20000−2i2i000
χ4422-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-2000000000−2i2i0000−2i2i-220000000000−2i2i000000000000000-2200002i−2i000
χ4544444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-21111111114004000-2-2000000-2-211-2000000000110000000000000000000000
χ4644444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-2111111111-400-40002200000022-1-12000000000-1-10000000000000000000000
χ4744444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1400-400022000000-2-2112000000000-1-10000000000000000000000
χ4844444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1-4004000-2-200000022-1-1-2000000000110000000000000000000000
χ494444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-2001-24-2-211-2-21111111040040000-2-2000000000-2-200-20000001111000000000000000000
χ504444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-2001-24-2-211-2-211111110-400-400002200000000022002000000-1-1-1-1000000000000000000
χ514444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-20012-422-1-122111-1-1-1-10400-4000022000000000-2200-200000011-1-1000000000000000000
χ524444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-20012-422-1-122111-1-1-1-10-40040000-2-20000000002-2002000000-1-111000000000000000000
χ534444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-2441-2-211-2-2-2-2111111100400-2-20000-2-2000000000-2-201111000000000000000000000000
χ544444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-2-4-41-2-211-2-2-2-2111111100-40022000022000000000220-1-1-1-1000000000000000000000000
χ554444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-244122-1-12222111-1-1-1-100-400-2-20000-2-200000000022011-1-1000000000000000000000000
χ564444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-2-4-4122-1-12222111-1-1-1-10040022000022000000000-2-20-1-111000000000000000000000000
χ5744-4-444-24-222-4-44-4-404-2-20042-22-4-4-22200-200000000-222000000000000000004-4000000000000000000000000000-22000000000
χ5844-4-444-24-222-4-44-4-404-2-20042-22-4-4-22200-200000000-22200000000000000000-440000000000000000000000000002-2000000000
χ5944-4-44-24-24-4-4-424-420-24-200-2-4-22224-424i−4i-200000000-222000000000−2i2i00004i−4i000000000000−2i2i00000000000000000000000000
χ6044-4-44-24-24-4-4-424-420-24-200-2-4-22224-42−4i4i-200000000-2220000000002i−2i0000−4i4i0000000000002i−2i00000000000000000000000000
χ6144-4-4-24444-4-42-4-22-40-2-2400-224-422-22-44i−4i-200000000-2220000000004i−4i0000−2i2i000000000000−2i2i00000000000000000000000000
χ6244-4-4-24444-4-42-4-22-40-2-2400-224-422-22-4−4i4i-200000000-222000000000−4i4i00002i−2i0000000000002i−2i00000000000000000000000000
χ6344-4-4-2-24-24-4-422-22201-2-20012-22-1-1-2224i−4i1003-300001-1-133-3-300000−2i2i0000−2i2i000000000000i−i3i−3i000000000000000000000000
χ6444-4-4-2-24-24-4-422-22201-2-20012-22-1-1-2224i−4i100-3300001-1-1-3-33300000−2i2i0000−2i2i000000000000i−i−3i3i000000000000000000000000
χ6544-4-4-2-24-24-4-422-22201-2-20012-22-1-1-222−4i4i1003-300001-1-133-3-3000002i−2i00002i−2i000000000000−ii−3i3i000000000000000000000000
χ6644-4-4-2-24-24-4-422-22201-2-20012-22-1-1-222−4i4i100-3300001-1-1-3-333000002i−2i00002i−2i000000000000−ii3i−3i000000000000000000000000
χ674-44-4444-4-44-44-4-4-44044400-4-4-444-4-44-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-42-224-4-4-4404-2-200-422-24-42-2200-2000000002-22000000000000000000000000000000000000000000000000−2i32i30000000
χ694-44-444-2-42-224-4-4-4404-2-200-422-24-42-2200-2000000002-220000000000000000000000000000000000000000000000002i3−2i30000000
χ704-44-44-242-44-442-4-4-20-24-2002-42-2-22-44200-2000000002-2200000000000000000000000000000000000000000000−2i32i300000000000
χ714-44-44-242-44-442-4-4-20-24-2002-42-2-22-44200-2000000002-22000000000000000000000000000000000000000000002i3−2i300000000000
χ724-44-4-244-4-44-4-2-42240-2-240022-44-222-2-400-2000000002-220000000000000000000000000000000000000000000000000023−2300000
χ734-44-4-244-4-44-4-2-42240-2-240022-44-222-2-400-2000000002-2200000000000000000000000000000000000000000000000000−232300000
χ744-4-44444-4-4-44-44-44-4044400-44-4-4-44-4-4400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-422-2-44-44-404-2-2−2i32i3-4-222-4422-200-20000−2i32i3−2i32i322-2−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ764-4-4444-2-422-2-44-44-404-2-22i3−2i3-4-222-4422-200-200002i3−2i32i3−2i322-22i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ774-4-444-242-4-44-4-2-4420-24-20024222-2-4-4-200-20000000022-200000000000−2i32i300000000000000000000−2i32i30000000000000000000000
χ784-4-444-242-4-44-4-2-4420-24-20024222-2-4-4-200-20000000022-2000000000002i3−2i3000000000000000000002i3−2i30000000000000000000000
χ794-4-444-2-2222-2-4-2-4420-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i30000000−2i32i3000000003-30000000000i3−i30000000000000000000000
χ804-4-444-2-2222-2-4-2-4420-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i300000002i3−2i300000000-330000000000−i3i30000000000000000000000
χ814-4-444-2-2222-2-4-2-4420-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i30000000−2i32i300000000-330000000000i3−i30000000000000000000000
χ824-4-444-2-2222-2-4-2-4420-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i300000002i3−2i3000000003-30000000000−i3i30000000000000000000000
χ834-4-44-244-4-4-44242-2-40-2-24002-2-4-42-222400-20000000022-2000000000000023−23000000000000000000000023−23000000000000000000
χ844-4-44-244-4-4-44242-2-40-2-24002-2-4-42-222400-20000000022-20000000000000−23230000000000000000000000−2323000000000000000000
χ854-4-44-24-2-422-2242-2-40-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i300000000023−23000000000000000000003i−3i−33000000000000000000
χ864-4-44-24-2-422-2242-2-40-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i3000000000−232300000000000000000000−3i3i3−3000000000000000000
χ874-4-44-24-2-422-2242-2-40-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i300000000023−2300000000000000000000−3i3i−33000000000000000000
χ884-4-44-24-2-422-2242-2-40-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i3000000000−2323000000000000000000003i−3i3−3000000000000000000
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
χ9188-8-88-4-4-4-444-848-840-4-4200-442-244-44-2002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-48-4444-8-44-80-42-400-4-2-44442-24002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-44444-4440222002-22-2-2-22-2-200-1006-60000-111-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-44444-4440222002-22-2-2-22-2-200-100-660000-11133-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-444-4484-8-8-40-4-420044-22-444-4-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-84-44-4-84480-42-4004-24-4-44-22400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-484-88-8-4444-402-4-400-244-42-24-4400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444-44-4444-4022200-2-2-222-2-22-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-444-44-4444-4022200-2-2-222-2-22-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8-884-44-4402-4-400-2-444-2244-400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-44-440222−4i34i3-22-2-2-22-2-2200-100002i3−2i32i3−2i311-1−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-44-4402224i3−4i3-22-2-2-22-2-2200-10000−2i32i3−2i32i311-1i3−i3i3−i300000000000000000000000000000000000000000000000000000

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