Finite Group Databasebeta

← Group #11781638

Character table — Group #11781638

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222244444444444444444888888888888888888888881212121212121212121212122424242424242424242424244848487272144
order122233444466666612121212346661212121212121212121212128812121212122424242424242424242424242424242488882424242424242424246688121224242424266884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-111-1
χ61111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11
χ81111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1
χ92222222-2-22222222-2-2-2-22-2222222-2-2-2-2-2-2-2-2200-222-2-200000000000000000000000000002-22200-2-20000000000
χ102222222-2-22222222-2-2-2-22-2222222-2-2-2-2-2-2-2-2200-222-2-20000000000000000000000000000-22-2-200220000000000
χ11222222-222-222222222222-2222-2-2-22-2-222222-200-2-2-2-2-2000000000000000022-2-22222-2-2-2-2000000000000000000
χ12222222-222-222222222222-2222-2-2-22-2-222222-200-2-2-2-2-20000000000000000-2-222-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-2-2-222-2-2-2-2-2-22i−2i2-2-2222i2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i000000000000000000000000000000
χ14222222-2-2-2-2222222-2-2-2-222222-2-2-2-222-2-2-2-2-2-2−2i2i2-2-222−2i−2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i000000000000000000000000000000
χ1522222-1222222-1-1-122222-12-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000002200-1-1-1-12-1-1000
χ1622222-1222222-1-1-122222-12-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2001111-211000
χ1722222-1222222-1-1-122222-12-1-1-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-1-2-2-2-211111111111100000000000000002200-1-1-1-1-211000
χ1822222-1222222-1-1-122222-12-1-1-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-1-2-2-2-21111111111110000000000000000-2-20011112-1-1000
χ1922222-1-2-2-2-222-1-1-12-2-2-2-2-12-1-1-1-2-211221111112i−2i-111-1-12i2i−2i−2i−i−i−i−i−i−iiiiiii0000000000000000000033−3−30−i3i3000
χ2022222-1-2-2-2-222-1-1-12-2-2-2-2-12-1-1-1-2-211221111112i−2i-111-1-12i2i−2i−2i−i−i−i−i−i−iiiiiii00000000000000000000−3−3330i3−i3000
χ2122222-1-2-2-2-222-1-1-12-2-2-2-2-12-1-1-1-2-21122111111−2i2i-111-1-1−2i−2i2i2iiiiiii−i−i−i−i−i−i0000000000000000000033−3−30i3−i3000
χ2222222-1-2-2-2-222-1-1-12-2-2-2-2-12-1-1-1-2-21122111111−2i2i-111-1-1−2i−2i2i2iiiiiii−i−i−i−i−i−i00000000000000000000−3−3330−i3i3000
χ232222-122222-1-1222-1-1-1-1-1-12-1-1-1-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-100-1-10000000000
χ242222-122222-1-1222-1-1-1-1-1-12-1-1-1-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-21100110000000000
χ252222-122222-1-1222-1-1-1-1-1-12-1-1-1-1-122-1-1-1-12-1-12-2-22-1-1-1-11111-2-21111-2-211112222-1-1-1-1-1-1-1-1-2-21100110000000000
χ262222-122222-1-1222-1-1-1-1-1-12-1-1-1-1-122-1-1-1-12-1-12-2-22-1-1-1-11111-2-21111-2-21111-2-2-2-21111111122-1-100-1-10000000000
χ272222-122-2-22-1-1222-11111-1-2-1-1-1-1-12-21111-211200-2-1-1113−33−30033−3−30033−3−3000033−3−333−3−32-2-1-100110000000000
χ282222-122-2-22-1-1222-11111-1-2-1-1-1-1-12-21111-211200-2-1-1113−33−30033−3−30033−3−30000−3−333−3−333-221100-1-10000000000
χ292222-122-2-22-1-1222-11111-1-2-1-1-1-1-12-21111-211200-2-1-111−33−3300−3−33300−3−333000033−3−333−3−3-221100-1-10000000000
χ302222-122-2-22-1-1222-11111-1-2-1-1-1-1-12-21111-211200-2-1-111−33−3300−3−33300−3−3330000−3−333−3−3332-2-1-100110000000000
χ312222-12-222-2-1-1222-1-1-1-1-1-1-2-1-1-111-2211-1-12-1-1-200-21111−i3i3i3−i300−i3−i3i3i300i3i3−i3−i322-2-2-1-1-1-1111100−i3i300−i3i30000000000
χ322222-12-222-2-1-1222-1-1-1-1-1-1-2-1-1-111-2211-1-12-1-1-200-21111−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-2-2221111-1-1-1-100i3−i300i3−i30000000000
χ332222-12-222-2-1-1222-1-1-1-1-1-1-2-1-1-111-2211-1-12-1-1-200-21111i3−i3−i3i300i3i3−i3−i300−i3−i3i3i322-2-2-1-1-1-1111100i3−i300i3−i30000000000
χ342222-12-222-2-1-1222-1-1-1-1-1-1-2-1-1-111-2211-1-12-1-1-200-21111i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-2-2221111-1-1-1-100−i3i300−i3i30000000000
χ352222-12-2-2-2-2-1-1222-11111-12-1-1-111-2-2-1-111-211-22i−2i211-1-1−i−iii2i2i−i−i−i−i−2i−2iiiii000033−3−3−3−33300−i3i300i3−i30000000000
χ362222-12-2-2-2-2-1-1222-11111-12-1-1-111-2-2-1-111-211-22i−2i211-1-1−i−iii2i2i−i−i−i−i−2i−2iiiii0000−3−33333−3−300i3−i300−i3i30000000000
χ372222-12-2-2-2-2-1-1222-11111-12-1-1-111-2-2-1-111-211-2−2i2i211-1-1ii−i−i−2i−2iiiii2i2i−i−i−i−i000033−3−3−3−33300i3−i300−i3i30000000000
χ382222-12-2-2-2-2-1-1222-11111-12-1-1-111-2-2-1-111-211-2−2i2i211-1-1ii−i−i−2i−2iiiii2i2i−i−i−i−i0000−3−33333−3−300−i3i300i3−i30000000000
χ392-2-22220-220-2-22-2-22-2-222202-2-2000-200-2-2222000000000000000000000000002-200002-22-200002−2002−22−20002−20
χ402-2-22220-220-2-22-2-22-2-222202-2-2000-200-2-2222000000000000000000000000002-200002-22-20000−2200−22−22000−220
χ412-2-22220-220-2-22-2-22-2-222202-2-2000-200-2-222200000000000000000000000000-220000-22-2200002−2002−22−2000−220
χ422-2-22220-220-2-22-2-22-2-222202-2-2000-200-2-222200000000000000000000000000-220000-22-220000−2200−22−220002−20
χ4344444-24-4-4444-2-2-24-4-4-4-4-2-4-2-2-244-22-4-422222-2002-2-2220000000000000000000000000000000000000000000000
χ4444444-2-444-444-2-2-244444-2-4-2-2-2-4-42-2-4-4-2-2-2-2-2200222220000000000000000000000000000000000000000000000
χ454444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-2-211-211-244-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000000
χ464444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-2-211-211-2-4-4-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000000
χ474444-2-24-4-44-2-2-2-2-2-222221-4111-2-2-2222-1-12-1-1-200211-1-123−2323−2300−3−33300−3−333000000000000000000000000000000
χ484444-2-24-4-44-2-2-2-2-2-222221-4111-2-2-2222-1-12-1-1-200211-1-1−2323−23230033−3−30033−3−3000000000000000000000000000000
χ494444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-4111222-22211-2112002-1-1-1-1−2i32i32i3−2i300i3i3−i3−i300−i3−i3i3i3000000000000000000000000000000
χ504444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-4111222-22211-2112002-1-1-1-12i3−2i3−2i32i300−i3−i3i3i300i3i3−i3−i3000000000000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-22222141112222-2-2-1-12-1-124i−4i-2-1-111−2i−2i2i2i−2i−2iiiii2i2i−i−i−i−i000000000000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-22222141112222-2-2-1-12-1-12−4i4i-2-1-1112i2i−2i−2i2i2i−i−i−i−i−2i−2iiiii000000000000000000000000000000
χ5344-4-44400004-4-44-4-4000040-44-400000000000000000000000000000000000−2i22i200−2i22i2−2i22i20000000000000000000000
χ5444-4-44400004-4-44-4-4000040-44-4000000000000000000000000000000000002i2−2i2002i2−2i22i2−2i20000000000000000000000
χ5544-4-4-240000-22-44-4223−2323−23-202-2200000023−23023−23000000000000000000000000−2i22i2002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000000000
χ5644-4-4-240000-22-44-4223−2323−23-202-2200000023−23023−230000000000000000000000002i2−2i200−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000000000
χ5744-4-4-240000-22-44-42−2323−2323-202-22000000−23230−2323000000000000000000000000−2i22i2002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ230000000000000000000000
χ5844-4-4-240000-22-44-42−2323−2323-202-22000000−23230−23230000000000000000000000002i2−2i200−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ230000000000000000000000
χ594-44-444400-4-44-4-44-4000040-4-444-4400000000-40004-4000000000000000000000000000000000000000000000000
χ604-44-444-4004-44-4-44-4000040-4-44-44-4000000004000-44000000000000000000000000000000000000000000000000
χ614-44-44-2400-4-4422-2-40000-2022-24-4-2000000002000-220000006−66−66−66−66−66−6000000000000000000000000000000
χ624-44-44-2400-4-4422-2-40000-2022-24-4-2000000002000-22000000−66−66−66−66−66−66000000000000000000000000000000
χ634-44-44-2-4004-4422-2-40000-2022-2-44200000000-20002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ644-44-44-2-4004-4422-2-40000-2022-2-44200000000-20002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ654-44-4-24400-42-2-4-44223−23−2323-2022-2-224023−2323−230−2323-4000-2223−230000000000000000000000000000000000000000000000
χ664-44-4-24400-42-2-4-442−232323−23-2022-2-2240−2323−2323023−23-4000-22−23230000000000000000000000000000000000000000000000
χ674-44-4-24-40042-2-4-44223−23−2323-2022-22-2-40−232323−230−232340002-2−23230000000000000000000000000000000000000000000000
χ684-44-4-24-40042-2-4-442−232323−23-2022-22-2-4023−23−2323023−2340002-223−230000000000000000000000000000000000000000000000
χ694-44-4-2-2400-42-222-2223−23−232310-1-11-22-2023−23−3303−320001-1−3300006−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ236−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23000000000000000000000000000000
χ704-44-4-2-2400-42-222-2223−23−232310-1-11-22-2023−23−3303−320001-1−330000−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000000000
χ714-44-4-2-2400-42-222-22−232323−2310-1-11-22-20−23233−30−3320001-13−300006−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ236−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23000000000000000000000000000000
χ724-44-4-2-2400-42-222-22−232323−2310-1-11-22-20−23233−30−3320001-13−30000−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23000000000000000000000000000000
χ734-44-4-2-2-40042-222-2223−23−232310-1-112-220−2323−3303−3-2000-113−30000i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000000000
χ744-44-4-2-2-40042-222-2223−23−232310-1-112-220−2323−3303−3-2000-113−30000−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000000000
χ754-44-4-2-2-40042-222-22−232323−2310-1-112-22023−233−30−33-2000-11−330000i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000000000
χ764-44-4-2-2-40042-222-22−232323−2310-1-112-22023−233−30−33-2000-11−330000−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000000000
χ774-4-444404-40-4-44-4-4444-4-4404-4-400040044-4-4-4000000000000000000000000000000000000000000000000000000
χ784-4-444-204-40-4-4-222444-4-4-20-222000-200-2-2222000000000000000000000000000000000000000000006−6−66000000
χ794-4-444-204-40-4-4-222444-4-4-20-222000-200-2-222200000000000000000000000000000000000000000000−666−6000000
χ804-4-444-20-440-4-4-2224-4-444-20-22200020022-2-2-2000000000000000000000000000000000000000022−2200−22−22000000
χ814-4-444-20-440-4-4-2224-4-444-20-22200020022-2-2-20000000000000000000000000000000000000000−2222002−22−2000000
χ824-4-44-2404-40224-4-4-2-2-222-20-222000400-2-2-4220000000000000000000000000000000023−23−2323000000000000000000
χ834-4-44-2404-40224-4-4-2-2-222-20-222000400-2-2-42200000000000000000000000000000000−232323−23000000000000000000
χ844-4-44-240-440224-4-4-222-2-2-20-222000-400224-2-2000000000000000000000000004-40000-22-22000000000000000000
χ854-4-44-240-440224-4-4-222-2-2-20-222000-400224-2-200000000000000000000000000-4400002-22-2000000000000000000
χ8688-8-88-400008-84-44-80000-404-4400000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-40000-444-44443−4343−4320-22-2000000−23230−2323000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-40000-444-444−4343−434320-22-200000023−23023−23000000000000000000000000000000000000000000000000000000
χ898-8-88-4-408-8044-444-4-4-444202-2-2000-400224-2-2000000000000000000000000000000000000000000000000000000
χ908-8-88-4-40-88044-444-444-4-4202-2-2000400-2-2-422000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.