Finite Group Databasebeta

← Group #11792412

Character table — Group #11792412

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order1244222334446666121212121212366666666121212121212121212668812122424242424242424242424242424242422446666121212124444881212121212121212242424242244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-11
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-11-11
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-1
χ922222222-1222-1-12-122-1-1-1-1-12-1-1-1-1-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002200000000-1-1-1-10000
χ1022222222-1222-1-12-122-1-1-1-1-12-1-1-1-1-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111110000-2-20000000011110000
χ1122222222-1222-1-12-122-1-1-1-1-12-1-1-1-1-12222-1-1-1-12-1-1-1-1-2-2-1-11111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000-2-20000000011110000
χ1222222222-1222-1-12-122-1-1-1-1-12-1-1-1-1-12222-1-1-1-12-1-1-1-1-2-2-1-11111-2-2-2-211111111-2-2-2-21111111100002200000000-1-1-1-10000
χ132222222-1222222-12-1-12222-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000222200-1-1-1-1-1-1-1-100000000
χ142222222-1222222-12-1-12222-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2001111111100000000
χ152222222-1222222-12-1-12222-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-2-2-1-1-2-2-2-211111111111100000000000022-2-200-1-1-1-1111100000000
χ162222222-1222222-12-1-12222-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2111111111111000000000000-2-222001111-1-1-1-100000000
χ1722222-2-222-2-22222222222222-2-2222-2-2-2-2-2-222222-2-22-2-2-222-2-222-2-22222-2-2-2-20000000000000000000000000000000000
χ1822222-2-222-2-22222222222222-2-2222-2-2-2-2-2-222222-2-2-22-2-2-2-222-2-222-2-2-2-222220000000000000000000000000000000000
χ1922222-2-22-1-2-22-1-12-122-1-1-1-1-1211-1-1-1-2-2-2-211-1-12-1-1112-211-1-11122-2-2-1-1-1-111110000−i3−i3i3i3−i3−i3i3i300000000000000−i3−i3i3i30000
χ2022222-2-22-1-2-22-1-12-122-1-1-1-1-1211-1-1-1-2-2-2-211-1-12-1-1112-211-1-11122-2-2-1-1-1-111110000i3i3−i3−i3i3i3−i3−i300000000000000i3i3−i3−i30000
χ2122222-2-22-1-2-22-1-12-122-1-1-1-1-1211-1-1-1-2-2-2-211-1-12-1-111-221111-1-1-2-2221111-1-1-1-10000−i3−i3i3i3−i3−i3i3i300000000000000i3i3−i3−i30000
χ2222222-2-22-1-2-22-1-12-122-1-1-1-1-1211-1-1-1-2-2-2-211-1-12-1-111-221111-1-1-2-2221111-1-1-1-10000i3i3−i3−i3i3i3−i3−i300000000000000−i3−i3i3i30000
χ2322222-2-2-12-2-2222-12-1-12222-1-1-2-2-1-1-11111-2-2-1-1-1-1-1112-21122-2-2-1-111-1-1-1-1111100000000000000000033−3−333−3−300000000
χ2422222-2-2-12-2-2222-12-1-12222-1-1-2-2-1-1-11111-2-2-1-1-1-1-1112-21122-2-2-1-111-1-1-1-11111000000000000000000−3−333−3−33300000000
χ2522222-2-2-12-2-2222-12-1-12222-1-1-2-2-1-1-11111-2-2-1-1-1-1-111-2211-2-22211-1-11111-1-1-1-100000000000000000033−3−3−3−33300000000
χ2622222-2-2-12-2-2222-12-1-12222-1-1-2-2-1-1-11111-2-2-1-1-1-1-111-2211-2-22211-1-11111-1-1-1-1000000000000000000−3−33333−3−300000000
χ272222-22-2222-2-2-2-22222-2-2222-22-2-2-222-22-22-222-2-2-22-2002-20000000000000000000000000000002-20000002-22-200000000
χ282222-22-2222-2-2-2-22222-2-2222-22-2-2-222-22-22-222-2-2-22-2002-2000000000000000000000000000000-22000000-22-2200000000
χ292222-22-2-122-2-2-2-2-12-1-1-2-222-112-211-1-11-112-2-1-1111-1100-1100003−33−333−3−333−3−3000000000000002-2003−33−3-11-1100000000
χ302222-22-2-122-2-2-2-2-12-1-1-2-222-112-211-1-11-112-2-1-1111-1100-1100003−33−333−3−333−3−300000000000000-2200−33−331-11-100000000
χ312222-22-2-122-2-2-2-2-12-1-1-2-222-112-211-1-11-112-2-1-1111-1100-110000−33−33−3−333−3−333000000000000002-200−33−33-11-1100000000
χ322222-22-2-122-2-2-2-2-12-1-1-2-222-112-211-1-11-112-2-1-1111-1100-110000−33−33−3−333−3−33300000000000000-22003−33−31-11-100000000
χ332222-2-2222-22-2-2-22222-2-2222-2-22-2-22-22-22-2222-2-2-2-2200-2200000000000000000000000000002-200002-2-22000000000000
χ342222-2-2222-22-2-2-22222-2-2222-2-22-2-22-22-22-2222-2-2-2-2200-220000000000000000000000000000-220000-222-2000000000000
χ352222-2-22-12-22-2-2-2-12-1-1-2-222-11-2211-11-11-1-22-1-11111-1001-100003−3−3333−3−3−3−3330000000000002-20000-111-1−333−300000000
χ362222-2-22-12-22-2-2-2-12-1-1-2-222-11-2211-11-11-1-22-1-11111-1001-100003−3−3333−3−3−3−333000000000000-2200001-1-113−3−3300000000
χ372222-2-22-12-22-2-2-2-12-1-1-2-222-11-2211-11-11-1-22-1-11111-1001-10000−333−3−3−33333−3−30000000000002-20000-111-13−3−3300000000
χ382222-2-22-12-22-2-2-2-12-1-1-2-222-11-2211-11-11-1-22-1-11111-1001-10000−333−3−3−33333−3−3000000000000-2200001-1-11−333−300000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-2000000000000000022-2-22222-2-2-2-20000000000000000000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-20000000000000000-2-222-2-2-2-222220000000000000000000000
χ4122-2-22222-1-2-2-2-1-12-1-2-21111-12-1-1-1-1-122-2-21111-211-1-100113−33−300003−33−33−33−322-2-2-1-1-1-11111000000000000003−33−30000
χ4222-2-22222-1-2-2-2-1-12-1-2-21111-12-1-1-1-1-122-2-21111-211-1-100113−33−300003−33−33−33−3-2-2221111-1-1-1-100000000000000−33−330000
χ4322-2-22222-1-2-2-2-1-12-1-2-21111-12-1-1-1-1-122-2-21111-211-1-10011−33−330000−33−33−33−3322-2-2-1-1-1-1111100000000000000−33−330000
χ4422-2-22222-1-2-2-2-1-12-1-2-21111-12-1-1-1-1-122-2-21111-211-1-10011−33−330000−33−33−33−33-2-2221111-1-1-1-1000000000000003−33−30000
χ4522-2-22-2-22222-22222-2-2-2-2-2-222-2-2222-2-22222-2-2-2-2-2-2-20022000000000000000000000000000000002i−2i000000002i−2i−2i2i0000
χ4622-2-22-2-22222-22222-2-2-2-2-2-222-2-2222-2-22222-2-2-2-2-2-2-2002200000000000000000000000000000000−2i2i00000000−2i2i2i−2i0000
χ4722-2-22-2-22-122-2-1-12-1-2-21111-1211-1-1-1-2-222-1-111-2111100-1-13−3−3300003−33−3−33−330000−i3−i3i3i3i3i3−i3−i300002i−2i00000000−iii−i0000
χ4822-2-22-2-22-122-2-1-12-1-2-21111-1211-1-1-1-2-222-1-111-2111100-1-13−3−3300003−33−3−33−330000i3i3−i3−i3−i3−i3i3i30000−2i2i00000000i−i−ii0000
χ4922-2-22-2-22-122-2-1-12-1-2-21111-1211-1-1-1-2-222-1-111-2111100-1-1−333−30000−33−333−33−30000−i3−i3i3i3i3i3−i3−i30000−2i2i00000000i−i−ii0000
χ5022-2-22-2-22-122-2-1-12-1-2-21111-1211-1-1-1-2-222-1-111-2111100-1-1−333−30000−33−333−33−30000i3i3−i3−i3−i3−i3i3i300002i−2i00000000−iii−i0000
χ5122-2-2-22-222-222-2-222-2-222-2-22-22-2-2-222-2-22-22-2-22222-200-220000000000000000000000000000000000000000000000020-2
χ5222-2-2-22-222-222-2-222-2-222-2-22-22-2-2-222-2-22-22-2-22222-200-2200000000000000000000000000000000000000000000000-202
χ5322-2-2-2-22222-22-2-222-2-222-2-22-2-22-2-22-222-22-2-2-2222-22002-2000000000000000000000000000000000000000000000020-20
χ5422-2-2-2-22222-22-2-222-2-222-2-22-2-22-2-22-222-22-2-2-2222-22002-20000000000000000000000000000000000000000000000-2020
χ554444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2111-2-2-2-2-2-211-211114411-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000
χ564444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2111-2-2-2-2-2-211-21111-4-41122222222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ5744444-4-4-2-2-4-44-2-2-2-2-2-2-2-2-2-21-22211122222211-211-1-14-4-1-1-2-222-2-2221111-1-1-1-10000000000000000000000000000000000
χ5844444-4-4-2-2-4-44-2-2-2-2-2-2-2-2-2-21-22211122222211-211-1-1-44-1-122-2-222-2-2-1-1-1-111110000000000000000000000000000000000
χ594444-44-44-24-4-4224-24422-2-2-2-4-2222-24-44-4-22-2-2-422-2200-2200000000000000000000000000000000000000000000000000
χ604444-44-4-2-24-4-422-2-2-2-222-2-212-22-1-11-22-22-22112-1-11-1001-1000023−2323−23−3−333−3−3330000000000000000000000000000000000
χ614444-44-4-2-24-4-422-2-2-2-222-2-212-22-1-11-22-22-22112-1-11-1001-10000−2323−232333−3−333−3−30000000000000000000000000000000000
χ624444-4-444-2-44-4224-24422-2-2-2-42-222-2-44-442-2-2-2-4222-2002-200000000000000000000000000000000000000000000000000
χ634444-4-44-2-2-44-422-2-2-2-222-2-2122-2-1-112-22-22-2112-1-1-1100-11000023−23−2323−3−33333−3−30000000000000000000000000000000000
χ644444-4-44-2-2-44-422-2-2-2-222-2-2122-2-1-112-22-22-2112-1-1-1100-110000−232323−2333−3−3−3−3330000000000000000000000000000000000
χ6544-4-4444-24-4-4-444-2422-4-4-4-4-2-244-2-2-2-2-222-4-422222-2-2002200000000000000000000000000000000000000000000000000
χ6644-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2111-2-22222-1-12-1-11100-1-123−2323−230000−33−33−33−330000000000000000000000000000000000
χ6744-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2111-2-22222-1-12-1-11100-1-1−2323−232300003−33−33−33−30000000000000000000000000000000000
χ6844-4-44-4-4-2444-444-2422-4-4-4-4-2-2-4-4-2-2-222-2-244222222200-2-200000000000000000000000000000000000000000000000000
χ6944-4-44-4-4-2-244-4-2-2-2-22222221-22211122-2-2-2-2-1-12-1-1-1-1001123−23−23230000−33−333−33−30000000000000000000000000000000000
χ7044-4-44-4-4-2-244-4-2-2-2-22222221-22211122-2-2-2-2-1-12-1-1-1-10011−232323−2300003−33−3−33−330000000000000000000000000000000000
χ7144-4-4-44-44-2-444224-2-4-4-2-222-2-4-2222-24-4-442-2224-2-2-22002-200000000000000000000000000000000000000000000000000
χ7244-4-4-44-4-24-444-4-4-242244-4-4-224-422-2-222-2-4422-2-2-2-22002-200000000000000000000000000000000000000000000000000
χ7344-4-4-44-4-2-2-44422-2-222-2-22212-22-1-11-222-22-2-1-1-2111-100-11000000003-3-333-3-330000000000000000000000000000000000
χ7444-4-4-44-4-2-2-44422-2-222-2-22212-22-1-11-222-22-2-1-1-2111-100-1100000000-333-3-333-30000000000000000000000000000000000
χ7544-4-4-4-444-24-44224-2-4-4-2-222-2-42-222-2-444-4-22224-2-22-200-2200000000000000000000000000000000000000000000000000
χ7644-4-4-4-44-244-44-4-4-242244-4-4-22-4422-22-2-224-422-2-2-22-200-2200000000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-24-4422-2-222-2-222122-2-1-112-2-22-22-1-1-211-11001-1000000003-3-33-333-30000000000000000000000000000000000
χ7844-4-4-4-44-2-24-4422-2-222-2-222122-2-1-112-2-22-22-1-1-211-11001-100000000-333-33-3-330000000000000000000000000000000000
χ794-44i−4i0004400000-4-44i−4i004i−4i400000-40000004i−4i00000000000000000000000002-22i−2i2-22-22i−2i2i−2i0000000000000000000000
χ804-44i−4i0004400000-4-44i−4i004i−4i400000-40000004i−4i0000000000000000000000000-22−2i2i-22-22−2i2i−2i2i0000000000000000000000
χ814-44i−4i0004-2000−2i32i3-424i−4i23−23−2i2i-2000−2i32i32000000−2i2i023−2300000000000000000000002-22i−2i−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ824-44i−4i0004-2000−2i32i3-424i−4i23−23−2i2i-2000−2i32i32000000−2i2i023−230000000000000000000000-22−2i2i1−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ834-44i−4i0004-20002i3−2i3-424i−4i−2323−2i2i-20002i3−2i32000000−2i2i0−232300000000000000000000002-22i−2i−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ844-44i−4i0004-20002i3−2i3-424i−4i−2323−2i2i-20002i3−2i32000000−2i2i0−23230000000000000000000000-22−2i2i1+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ854-4−4i4i0004400000-4-4−4i4i00−4i4i400000-4000000−4i4i00000000000000000000000002-2−2i2i2-22-2−2i2i−2i2i0000000000000000000000
χ864-4−4i4i0004400000-4-4−4i4i00−4i4i400000-4000000−4i4i0000000000000000000000000-222i−2i-22-222i−2i2i−2i0000000000000000000000
χ874-4−4i4i0004-2000−2i32i3-42−4i4i−23232i−2i-2000−2i32i320000002i−2i0−232300000000000000000000002-2−2i2i−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ884-4−4i4i0004-2000−2i32i3-42−4i4i−23232i−2i-2000−2i32i320000002i−2i0−23230000000000000000000000-222i−2i1−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ894-4−4i4i0004-20002i3−2i3-42−4i4i23−232i−2i-20002i3−2i320000002i−2i023−2300000000000000000000002-2−2i2i−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ904-4−4i4i0004-20002i3−2i3-42−4i4i23−232i−2i-20002i3−2i320000002i−2i023−230000000000000000000000-222i−2i1+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ918-88i−8i000-48000004-8−4i4i008i−8i-4000004000000−4i4i00000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-4000−4i34i344−4i4i43−43−4i4i20002i3−2i3-20000002i−2i0−232300000000000000000000000000000000000000000000000000000000
χ938-88i−8i000-4-40004i3−4i344−4i4i−4343−4i4i2000−2i32i3-20000002i−2i023−2300000000000000000000000000000000000000000000000000000000
χ948-8−8i8i000-48000004-84i−4i00−8i8i-40000040000004i−4i00000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000−4i34i3444i−4i−43434i−4i20002i3−2i3-2000000−2i2i023−2300000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-40004i3−4i3444i−4i43−434i−4i2000−2i32i3-2000000−2i2i0−232300000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.