Finite Group Databasebeta

← Group #11787114

Character table — Group #11787114

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444444448888888888888888888888121212121212121224242424242424242424242424242424242424243636363636363636
order1244222334446612121212366666666612121212121212121212446612121212121212121212121212121212121222448888446688121212121212242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-11-11-1ii−i−i1-11-1i−i1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-11-11-1−i−iii1-11-1−ii1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1-11-11ii−i−i-11-11i−i-11-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1-11-11−i−iii-11-11−ii-11-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111-11-1ii−i−i-111-1−ii1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111-11-1−i−iii-111-1i−i1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-11-11ii−i−i1-1-11−ii-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-111111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-11-11−i−iii1-1-11i−i-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222-12222-1-1-122-122-12-1-1-1-1-122-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222000022-1-100-1-1-1-1-1-10000000000000000
χ1822222222-12222-1-1-122-122-12-1-1-1-1-122-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-20000-2-211001111110000000000000000
χ1922222222-12222-1-1-122-122-12-1-1-1-1-122-1-1-1-1-1-1-12-2-2-1-1-1-1-2-2111111-2-211111122220000-2-2-1-100-1-111110000000000000000
χ2022222222-12222-1-1-122-122-12-1-1-1-1-122-1-1-1-1-1-1-12-2-2-1-1-1-1-2-2111111-2-2111111-2-2-2-2000022110011-1-1-1-10000000000000000
χ212222222-12222-1222-1-1-1-1-12-12-1-1-12-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100002222000022000000-1-1-1-1-1-1-1-100000000
χ222222222-12222-1222-1-1-1-1-12-12-1-1-12-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-20000-2-20000001111111100000000
χ232222222-12222-1222-1-1-1-1-12-12-1-1-12-1-1222-1-1-1-1-1-2-2-1-1-1-111-2-2111111-2-21111000022220000-2-2000000-1-1-1-1111100000000
χ242222222-12222-1222-1-1-1-1-12-12-1-1-12-1-1222-1-1-1-1-1-2-2-1-1-1-111-2-2111111-2-211110000-2-2-2-20000220000001111-1-1-1-100000000
χ2522222-2-222-2-2222222222-22-2-22-2-2-2-2-22-2-222-2-22002-22-200000000000000002-2-220000002-200-2200000000000000000000
χ2622222-2-222-2-2222222222-22-2-22-2-2-2-2-22-2-222-2-22002-22-20000000000000000-222-2000000-22002-200000000000000000000
χ2722222-2-22-1-2-222-1-1-122-12-2-1-21-1111-2-2-111-1-111200-11-11003−333−3−3003−333−3−32-2-22000000-11001-13−33−30000000000000000
χ2822222-2-22-1-2-222-1-1-122-12-2-1-21-1111-2-2-111-1-111200-11-11003−333−3−3003−333−3−3-222-20000001-100-11−33−330000000000000000
χ2922222-2-22-1-2-222-1-1-122-12-2-1-21-1111-2-2-111-1-111200-11-1100−33−3−33300−33−3−3332-2-22000000-11001-1−33−330000000000000000
χ3022222-2-22-1-2-222-1-1-122-12-2-1-21-1111-2-2-111-1-111200-11-1100−33−3−33300−33−3−333-222-20000001-100-113−33−30000000000000000
χ312222-22-2222-2-22222222-2-2-222222-22-2-22-22222-200-2-2-2-2000000000000000000000000000000000000000000002-22-20000
χ322222-22-2222-2-22222222-2-2-222222-22-2-22-22222-200-2-2-2-200000000000000000000000000000000000000000000-22-220000
χ332222-2-2222-22-22222222-22-2-2-22-2-22-22-2-2222-2-2-200-22-22000000000000000000002-22-20000000000002-22-2000000000000
χ342222-2-2222-22-22222222-22-2-2-22-2-22-22-2-2222-2-2-200-22-2200000000000000000000-22-22000000000000-22-22000000000000
χ352222-2-22-12-22-2-1222-1-1-11-1-21-2-11121-1-2-22-1-1111001-11-13−3003−33−33−3003−33−300002-22-2000000000000-11-113−33−300000000
χ362222-2-22-12-22-2-1222-1-1-11-1-21-2-11121-1-2-22-1-1111001-11-13−3003−33−33−3003−33−30000-22-220000000000001-11-1−33−3300000000
χ372222-2-22-12-22-2-1222-1-1-11-1-21-2-11121-1-2-22-1-1111001-11-1−3300−33−33−3300−33−3300002-22-2000000000000-11-11−33−3300000000
χ382222-2-22-12-22-2-1222-1-1-11-1-21-2-11121-1-2-22-1-1111001-11-1−3300−33−33−3300−33−330000-22-220000000000001-11-13−33−300000000
χ3922-2-22222-1-2-2-22-111-2-2-122-12-1-1-1-1-1-2-21111111-22-2-1-11122-1-1-1-1-1-1-2-21111112-22-200002-2-1100-11-1-1110000000000000000
χ4022-2-22222-1-2-2-22-111-2-2-122-12-1-1-1-1-1-2-21111111-22-2-1-11122-1-1-1-1-1-1-2-2111111-22-220000-221-1001-111-1-10000000000000000
χ4122-2-22222-1-2-2-22-111-2-2-122-12-1-1-1-1-1-2-21111111-2-22-1-111-2-211111122-1-1-1-1-1-12-22-20000-22-1100-1111-1-10000000000000000
χ4222-2-22222-1-2-2-22-111-2-2-122-12-1-1-1-1-1-2-21111111-2-22-1-111-2-211111122-1-1-1-1-1-1-22-2200002-21-1001-1-1-1110000000000000000
χ4322-2-2222-12-2-2-2-12-2-211-1-1-12-12-1-1-1211-2-2-2111112-2-1-111-1-122-1-1-1-111-2-2111100002i2i−2i−2i00002i−2i000000−i−iii−i−iii00000000
χ4422-2-2222-12-2-2-2-12-2-211-1-1-12-12-1-1-1211-2-2-2111112-2-1-111-1-122-1-1-1-111-2-211110000−2i−2i2i2i0000−2i2i000000ii−i−iii−i−i00000000
χ4522-2-2222-12-2-2-2-12-2-211-1-1-12-12-1-1-1211-2-2-211111-22-1-11111-2-21111-1-122-1-1-1-100002i2i−2i−2i0000−2i2i000000−i−iiiii−i−i00000000
χ4622-2-2222-12-2-2-2-12-2-211-1-1-12-12-1-1-1211-2-2-211111-22-1-11111-2-21111-1-122-1-1-1-10000−2i−2i2i2i00002i−2i000000ii−i−i−i−iii00000000
χ4722-2-22-2-22222-222-2-2-2-222-22-2-22-2-2-222-222-2-222-2002-2-22000000000000000022-2-20000002200-2-200000000000000000000
χ4822-2-22-2-22222-222-2-2-2-222-22-2-22-2-2-222-222-2-222-2002-2-220000000000000000-2-222000000-2-2002200000000000000000000
χ4922-2-22-2-22-122-22-111-2-2-12-2-1-21-1111221-1-111-1-1-200-111-1003−333−3−300−33−3−33322-2-2000000-1-100113−3−330000000000000000
χ5022-2-22-2-22-122-22-111-2-2-12-2-1-21-1111221-1-111-1-1-200-111-1003−333−3−300−33−3−333-2-2220000001100-1-1−333−30000000000000000
χ5122-2-22-2-22-122-22-111-2-2-12-2-1-21-1111221-1-111-1-1-200-111-100−33−3−333003−333−3−322-2-2000000-1-10011−333−30000000000000000
χ5222-2-22-2-22-122-22-111-2-2-12-2-1-21-1111221-1-111-1-1-200-111-100−33−3−333003−333−3−3-2-2220000001100-1-13−3−330000000000000000
χ5322-2-2-22-222-22222-2-2-2-22-2-2-222222-2-222-22-2-2-2-2200-2-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5422-2-2-22-222-22222-2-2-2-22-2-2-222222-2-222-22-2-2-2-2200-2-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5522-2-2-2-22222-2222-2-2-2-22-22-2-2-22-2-222-222-2-2-222200-222-2000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000000
χ5622-2-2-2-22222-2222-2-2-2-22-22-2-2-22-2-222-222-2-2-222200-222-200000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000000
χ5722-2-2-2-22-122-22-12-2-211-11-1-21-2-1112-1122-211-1-1-1001-1-113−3003−33−3−3300−33−3300002i−2i−2i2i000000000000−iii−ii3−i3−i3i300000000
χ5822-2-2-2-22-122-22-12-2-211-11-1-21-2-1112-1122-211-1-1-1001-1-113−3003−33−3−3300−33−330000−2i2i2i−2i000000000000i−i−ii−i3i3i3−i300000000
χ5922-2-2-2-22-122-22-12-2-211-11-1-21-2-1112-1122-211-1-1-1001-1-11−3300−33−333−3003−33−300002i−2i−2i2i000000000000−iii−i−i3i3i3−i300000000
χ6022-2-2-2-22-122-22-12-2-211-11-1-21-2-1112-1122-211-1-1-1001-1-11−3300−33−333−3003−33−30000−2i2i2i−2i000000000000i−i−iii3−i3−i3i300000000
χ614444444-2-2444-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-2-21111-2441111-2-2-2-21111-2-2-2-21111000000000000000000000000000000000000
χ624444444-2-2444-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-2-21111-2-4-411112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ6344444-4-4-24-4-44-2444-2-2-2-2242-4-222-4224-4-4-2-222-200-22-220000000000000000000000000000000000000000000000000000
χ6444444-4-4-2-2-4-44-2-2-2-2-2-21-22-2221-1-1222-22211-1-1-2001-11-10023−23−3−3330023−23−3−333000000000000000000000000000000000000
χ6544444-4-4-2-2-4-44-2-2-2-2-2-21-22-2221-1-1222-22211-1-1-2001-11-100−232333−3−300−232333−3−3000000000000000000000000000000000000
χ664444-44-44-24-4-44-2-2-244-2-4-424-2-2-2-224-42-22-2-2-2-2-40022220000000000000000000000000000000000000000000000000000
χ674444-44-4-244-4-4-2444-2-2-222-4-24-2-2-2-4-22-44-4-2-2-2-220022220000000000000000000000000000000000000000000000000000
χ684444-44-4-2-24-4-4-2-2-2-2-2-21222-2-21112-222-221111200-1-1-1-100003-3-3300003-3-33000000000000000000000000000000000000
χ694444-44-4-2-24-4-4-2-2-2-2-2-21222-2-21112-222-221111200-1-1-1-10000-333-30000-333-3000000000000000000000000000000000000
χ704444-4-444-2-44-44-2-2-244-2-442-42-222-2-4422-2-2-222-4002-22-20000000000000000000000000000000000000000000000000000
χ714444-4-44-2-2-44-4-2-2-2-2-2-212-22221-1-1-22-222-211-1-1200-11-1123−2300−33−3323−2300−33−33000000000000000000000000000000000000
χ724444-4-44-2-2-44-4-2-2-2-2-2-212-22221-1-1-22-222-211-1-1200-11-11−2323003−33−3−2323003−33−3000000000000000000000000000000000000
χ7344-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2111-222222-1-1-1-124-411-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000000
χ7444-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2111-222222-1-1-1-12-4411-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000000
χ7544-4-44-4-4-2444-4-24-4-422-2-2242-4-222-4-2-2-44422-2-2200-222-20000000000000000000000000000000000000000000000000000
χ7644-4-44-4-4-2-244-4-2-222221-22-2221-1-12-2-22-2-2-1-1112001-1-110023−23−3−33300−232333−3−3000000000000000000000000000000000000
χ7744-4-44-4-4-2-244-4-2-222221-22-2221-1-12-2-22-2-2-1-1112001-1-1100−232333−3−30023−23−3−333000000000000000000000000000000000000
χ7844-4-4-44-44-2-4444-222-4-4-2-4-424-2-2-2-22-44-22-2222240022-2-20000000000000000000000000000000000000000000000000000
χ7944-4-4-44-4-24-444-24-4-422-222-4-24-2-2-2-42-24-442222-20022-2-20000000000000000000000000000000000000000000000000000
χ8044-4-4-44-4-2-2-444-2-222221222-2-211122-2-22-2-1-1-1-1-200-1-11100003-3-330000-333-3000000000000000000000000000000000000
χ8144-4-4-44-4-2-2-444-2-222221222-2-211122-2-22-2-1-1-1-1-200-1-1110000-333-300003-3-33000000000000000000000000000000000000
χ8244-4-4-4-444-24-444-222-4-4-2-442-42-222-24-4-2-2222-2-24002-2-220000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-2-24-44-2-2222212-22221-1-1-2-22-2-22-1-111-200-111-123−2300−33−33−2323003−33−3000000000000000000000000000000000000
χ8444-4-4-4-44-2-24-44-2-2222212-22221-1-1-2-22-2-22-1-111-200-111-1−2323003−33−323−2300−33−33000000000000000000000000000000000000
χ854-44i−4i00044000-4-44i−4i4i−4i400000-4000000004i−4i0000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ864-44i−4i00044000-4-44i−4i4i−4i400000-4000000004i−4i000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ874-4−4i4i00044000-4-4−4i4i−4i4i400000-400000000−4i4i000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ884-4−4i4i00044000-4-4−4i4i−4i4i400000-400000000−4i4i0000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ898-88i−8i0008-4000-84−4i4i8i−8i-400000400000000−4i4i0000000000000000000000000000000000000000000000000000000000000
χ908-88i−8i000-480004-88i−8i−4i4i-400000400000000−4i4i0000000000000000000000000000000000000000000000000000000000000
χ918-88i−8i000-4-400044−4i4i−4i4i200000-26-60000002i−2i6i−6i00000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-400044−4i4i−4i4i200000-2-660000002i−2i−6i6i00000000000000000000000000000000000000000000000000000000000
χ938-8−8i8i0008-4000-844i−4i−8i8i-4000004000000004i−4i0000000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i000-480004-8−8i8i4i−4i-4000004000000004i−4i0000000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000444i−4i4i−4i200000-26-6000000−2i2i−6i6i00000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-4000444i−4i4i−4i200000-2-66000000−2i2i6i−6i00000000000000000000000000000000000000000000000000000000000

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