Finite Group Databasebeta

← Group #11793862

Character table — Group #11793862

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order12442223344466661212121212123666666661212121212121212126688121224242424242424242424242424242424444412121212121212128888882424242424242424242424242244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
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
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-11-11
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ922222222-12222-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000002222000000-1-1-1-1-1-1-1-10000
χ1022222222-12222-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2000000111111110000
χ1122222222-12222-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-211111111111100000000000022-2-2000000-1-1-1-111110000
χ1222222222-12222-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2111111111111000000000000-2-2220000001111-1-1-1-10000
χ132222222-12222-12-1-1-1-122-1-1-1-1-1222-1-1-1-1-1-1-12-1-122-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ142222222-12222-12-1-1-1-122-1-1-1-1-1222-1-1-1-1-1-1-12-1-122-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111110000-2-21111000000000000
χ152222222-12222-12-1-1-1-122-1-1-1-1-1222-1-1-1-1-1-1-12-1-122-1-1-2-2-1-11111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000-2-21111000000000000
χ162222222-12222-12-1-1-1-122-1-1-1-1-1222-1-1-1-1-1-1-12-1-122-1-1-2-2-1-11111-2-2-2-211111111-2-2-2-211111111000022-1-1-1-1000000000000
χ1722222-2-2222-2-222-2-22222-2-222-22-2-2-2-222-222-2-2-22-22-2002-20000000000000000000000000000002i−2i00000000002i2i−2i−2i0000
χ1822222-2-2222-2-222-2-22222-2-222-22-2-2-2-222-222-2-2-22-22-2002-2000000000000000000000000000000−2i2i0000000000−2i−2i2i2i0000
χ1922222-2-22-12-2-22-1-2-222-1-1-2-2-12-2-11111-12-2-1-1111-11-1100-11000033−3−33333−3−3−3−3000000000000002i−2i000000−i3−i3i3i3−i−iii0000
χ2022222-2-22-12-2-22-1-2-222-1-1-2-2-12-2-11111-12-2-1-1111-11-1100-11000033−3−33333−3−3−3−300000000000000−2i2i000000i3i3−i3−i3ii−i−i0000
χ2122222-2-22-12-2-22-1-2-222-1-1-2-2-12-2-11111-12-2-1-1111-11-1100-110000−3−333−3−3−3−33333000000000000002i−2i000000i3i3−i3−i3−i−iii0000
χ2222222-2-22-12-2-22-1-2-222-1-1-2-2-12-2-11111-12-2-1-1111-11-1100-110000−3−333−3−3−3−3333300000000000000−2i2i000000−i3−i3i3i3ii−i−i0000
χ232222-22-222-22-222-2-22222-2-22-22-22-2-2-22-2222-2-2-2-22-2200-2200000000000000000000000000002i−2i000000002i−2i2i−2i00000000
χ242222-22-222-22-222-2-22222-2-22-22-22-2-2-22-2222-2-2-2-22-2200-220000000000000000000000000000−2i2i00000000−2i2i−2i2i00000000
χ252222-22-22-1-22-22-1-2-222-1-1-2-2-1-221-1111-1-22-1-11111-11-1001-100003−33−333−3−333−3−30000000000002i−2i00000000−ii−ii−i3i3−i3i30000
χ262222-22-22-1-22-22-1-2-222-1-1-2-2-1-221-1111-1-22-1-11111-11-1001-100003−33−333−3−333−3−3000000000000−2i2i00000000i−ii−ii3−i3i3−i30000
χ272222-22-22-1-22-22-1-2-222-1-1-2-2-1-221-1111-1-22-1-11111-11-1001-10000−33−33−3−333−3−3330000000000002i−2i00000000−ii−iii3−i3i3−i30000
χ282222-22-22-1-22-22-1-2-222-1-1-2-2-1-221-1111-1-22-1-11111-11-1001-10000−33−33−3−333−3−333000000000000−2i2i00000000i−ii−i−i3i3−i3i30000
χ292222-2-2222-2-2222222222222-2-2-2-22222-2-222222-2-2-2-22-2-2-222-2-22-2-2222-2-2-2-2220000000000000000000000000000000000
χ302222-2-2222-2-2222222222222-2-2-2-22222-2-222222-2-2-2-2-22-2-2-2-222-222-2-2-22222-2-20000000000000000000000000000000000
χ312222-2-222-1-2-222-12222-1-122-1-2-211-1-1-1-1-2-2-1-1-1-1-111112-21122-2-2-111-1-1-11111-1-100000000000000000000003−3−33−333−30000
χ322222-2-222-1-2-222-12222-1-122-1-2-211-1-1-1-1-2-2-1-1-1-1-111112-21122-2-2-111-1-1-11111-1-10000000000000000000000−333−33−3−330000
χ332222-2-222-1-2-222-12222-1-122-1-2-211-1-1-1-1-2-2-1-1-1-1-11111-2211-2-2221-1-1111-1-1-1-11100000000000000000000003−3−333−3−330000
χ342222-2-222-1-2-222-12222-1-122-1-2-211-1-1-1-1-2-2-1-1-1-1-11111-2211-2-2221-1-1111-1-1-1-1110000000000000000000000−333−3−333−30000
χ352222-2-22-12-2-22-12-1-1-1-122-1-1-111-2-22-1-1-111-1-12-1-1-2-2112-211-1-1112-2-22-1-11111-1-10000−i3−i3−i3−i3i3i3i3i3000000−i3−i3i3i3000000000000
χ362222-2-22-12-2-22-12-1-1-1-122-1-1-111-2-22-1-1-111-1-12-1-1-2-2112-211-1-1112-2-22-1-11111-1-10000i3i3i3i3−i3−i3−i3−i3000000i3i3−i3−i3000000000000
χ372222-2-22-12-2-22-12-1-1-1-122-1-1-111-2-22-1-1-111-1-12-1-1-2-211-221111-1-1-222-211-1-1-1-1110000−i3−i3−i3−i3i3i3i3i3000000i3i3−i3−i3000000000000
χ382222-2-22-12-2-22-12-1-1-1-122-1-1-111-2-22-1-1-111-1-12-1-1-2-211-221111-1-1-222-211-1-1-1-1110000i3i3i3i3−i3−i3−i3−i3000000−i3−i3i3i3000000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-2000000000000000000000000000000002i−2i2i−2i2i−2i000000000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-200000000000000000000000000000000−2i2i−2i2i−2i2i000000000000
χ4122-2-2222-12-2-2-2-12-1-111-2-211-1-1-1222-1-1-11111-211-2-2-1-100113−33−300003−33−33−33−30000−i3−i3i3i3−i3−i3i3i300002i−2i−ii−ii000000000000
χ4222-2-2222-12-2-2-2-12-1-111-2-211-1-1-1222-1-1-11111-211-2-2-1-100113−33−300003−33−33−33−30000i3i3−i3−i3i3i3−i3−i30000−2i2ii−ii−i000000000000
χ4322-2-2222-12-2-2-2-12-1-111-2-211-1-1-1222-1-1-11111-211-2-2-1-10011−33−330000−33−33−33−330000−i3−i3i3i3−i3−i3i3i30000−2i2ii−ii−i000000000000
χ4422-2-2222-12-2-2-2-12-1-111-2-211-1-1-1222-1-1-11111-211-2-2-1-10011−33−330000−33−33−33−330000i3i3−i3−i3i3i3−i3−i300002i−2i−ii−ii000000000000
χ4522-2-22-2-222-22222-2-2-2-2-2-22222-22-2-2-2-22-22-2-2222-222-200-22000000000000000000000000000000000000000000000020-20
χ4622-2-22-2-222-22222-2-2-2-2-2-22222-22-2-2-2-22-22-2-2222-222-200-220000000000000000000000000000000000000000000000-2020
χ4722-2-2-22-2222-2222-2-2-2-2-2-2222-22-22-2-2-222-2-2-22222-2-22002-20000000000000000000000000000000000000000000000020-2
χ4822-2-2-22-2222-2222-2-2-2-2-2-2222-22-22-2-2-222-2-2-22222-2-22002-200000000000000000000000000000000000000000000000-202
χ4922-2-2-2-222222-22222-2-2-2-2-2-22-2-2-2-2222222-2-2-2-2-222-2-20022000000000000000022-2-222-2-2-2-2220000000000000000000000
χ5022-2-2-2-222222-22222-2-2-2-2-2-22-2-2-2-2222222-2-2-2-2-222-2-200220000000000000000-2-222-2-22222-2-20000000000000000000000
χ5122-2-2-2-22-1222-2-12-1-111-2-211-111-2-22-1-1-1-1-111-211221100-1-13−3−3300003−3−33−333−322-2-2-1-11111-1-10000003−3−33000000000000
χ5222-2-2-2-22-1222-2-12-1-111-2-211-111-2-22-1-1-1-1-111-211221100-1-13−3−3300003−3−33−333−3-2-22211-1-1-1-111000000−333−3000000000000
χ5322-2-2-2-22-1222-2-12-1-111-2-211-111-2-22-1-1-1-1-111-211221100-1-1−333−30000−333−33−3−3322-2-2-1-11111-1-1000000−333−3000000000000
χ5422-2-2-2-22-1222-2-12-1-111-2-211-111-2-22-1-1-1-1-111-211221100-1-1−333−30000−333−33−3−33-2-22211-1-1-1-1110000003−3−33000000000000
χ554444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-211-211-2-2114411-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000
χ564444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-211-211-2-211-4-41122222222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ5744444-4-4-244-4-4-2422-2-24422-2-224-4-422-2-22-2-2-4224-4-2200-2200000000000000000000000000000000000000000000000000
χ5844444-4-4-2-24-4-4-2-222-2-2-2-2221-22-222-1-11-22112-1-1-221-1001-100002323−23−23−3−3−3−333330000000000000000000000000000000000
χ5944444-4-4-2-24-4-4-2-222-2-2-2-2221-22-222-1-11-22112-1-1-221-1001-10000−23−2323233333−3−3−3−30000000000000000000000000000000000
χ604444-44-4-24-44-4-2422-2-24422-22-2-44-422-22-2-2-2-422-442-2002-200000000000000000000000000000000000000000000000000
χ614444-44-4-2-2-44-4-2-222-2-2-2-22212-22-22-1-112-2112-1-12-2-1100-11000023−2323−23−3−333−3−3330000000000000000000000000000000000
χ624444-44-4-2-2-44-4-2-222-2-2-2-22212-22-22-1-112-2112-1-12-2-1100-110000−2323−232333−3−333−3−30000000000000000000000000000000000
χ634444-4-44-2-2-4-44-2-2-2-2-2-2-2-2-2-212222-21112211-21122-1-14-4-1-1-2-222-222-211-1-1-1-1110000000000000000000000000000000000
χ644444-4-44-2-2-4-44-2-2-2-2-2-2-2-2-2-212222-21112211-21122-1-1-44-1-122-2-22-2-22-1-11111-1-10000000000000000000000000000000000
χ6544-4-44444-2-4-4-44-244-4-422-4-4-244-2-2-2-2-2-2-4-42222222-2-2002200000000000000000000000000000000000000000000000000
χ6644-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2-2-211122-1-12-1-1221100-1-123−2323−230000−33−33−33−330000000000000000000000000000000000
χ6744-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2-2-211122-1-12-1-1221100-1-1−2323−232300003−33−33−33−30000000000000000000000000000000000
χ6844-4-44-4-44-2-4444-2-4-4-4-42244-24-4-22222-2-4422-2-2-22-2-22002-200000000000000000000000000000000000000000000000000
χ6944-4-44-4-4-24-444-242222-4-4-2-2-2-224-4-422-22-2224-2-2-44-22002-200000000000000000000000000000000000000000000000000
χ7044-4-44-4-4-2-2-444-2-2222222-2-21-22-222-1-112-2-1-1-2112-21-100-11000000003-33-3-33-330000000000000000000000000000000000
χ7144-4-44-4-4-2-2-444-2-2222222-2-21-22-222-1-112-2-1-1-2112-21-100-1100000000-33-333-33-30000000000000000000000000000000000
χ7244-4-4-44-44-24-444-2-4-4-4-42244-2-442-2222-24-422-2-2-2-222-200-2200000000000000000000000000000000000000000000000000
χ7344-4-4-44-4-244-44-242222-4-4-2-2-22-2-44-422-2-22224-2-24-42-200-2200000000000000000000000000000000000000000000000000
χ7444-4-4-44-4-2-24-44-2-2222222-2-212-22-22-1-11-22-1-1-211-22-11001-1000000003-3-333-3-330000000000000000000000000000000000
χ7544-4-4-44-4-2-24-44-2-2222222-2-212-22-22-1-11-22-1-1-211-22-11001-100000000-333-3-333-30000000000000000000000000000000000
χ7644-4-4-4-444-244-44-244-4-422-4-4-2-4-422-2-2-2-24422222-2-22200-2-200000000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-244-4-2-2-2-222222212222-2111-2-2-1-12-1-1-2-2-1-1001123−23−23230000−333−33−3−330000000000000000000000000000000000
χ7844-4-4-4-44-2-244-4-2-2-2-222222212222-2111-2-2-1-12-1-1-2-2-1-10011−232323−2300003−3−33−333−30000000000000000000000000000000000
χ794-44i−4i00044000-4-4004i−4i4i−4i0040000000-4004i−4i0000000000000000000000000002-22i−2i2-22i−2i2i−2i2-20000000000000000000000
χ804-44i−4i00044000-4-4004i−4i4i−4i0040000000-4004i−4i000000000000000000000000000-22−2i2i-22−2i2i−2i2i-220000000000000000000000
χ814-44i−4i000-240002-4−2i32i3−2i2i4i−4i23−23-200000−2i32i3200−2i2i023−230000000000000000000000002-22i−2i−1−i31+i32ζ11−2ζ112ζ7−2ζ7−1+i31−i30000000000000000000000
χ824-44i−4i000-240002-4−2i32i3−2i2i4i−4i23−23-200000−2i32i3200−2i2i023−23000000000000000000000000-22−2i2i1+i3−1−i3−2ζ112ζ11−2ζ72ζ71−i3−1+i30000000000000000000000
χ834-44i−4i000-240002-42i3−2i3−2i2i4i−4i−2323-2000002i3−2i3200−2i2i0−23230000000000000000000000002-22i−2i−1+i31−i32ζ7−2ζ72ζ11−2ζ11−1−i31+i30000000000000000000000
χ844-44i−4i000-240002-42i3−2i3−2i2i4i−4i−2323-2000002i3−2i3200−2i2i0−2323000000000000000000000000-22−2i2i1−i3−1+i3−2ζ72ζ7−2ζ112ζ111+i3−1−i30000000000000000000000
χ854-4−4i4i00044000-4-400−4i4i−4i4i0040000000-400−4i4i0000000000000000000000000002-2−2i2i2-2−2i2i−2i2i2-20000000000000000000000
χ864-4−4i4i00044000-4-400−4i4i−4i4i0040000000-400−4i4i000000000000000000000000000-222i−2i-222i−2i2i−2i-220000000000000000000000
χ874-4−4i4i000-240002-4−2i32i32i−2i−4i4i−2323-200000−2i32i32002i−2i0−23230000000000000000000000002-2−2i2i−1−i31+i3−2ζ112ζ11−2ζ72ζ7−1+i31−i30000000000000000000000
χ884-4−4i4i000-240002-4−2i32i32i−2i−4i4i−2323-200000−2i32i32002i−2i0−2323000000000000000000000000-222i−2i1+i3−1−i32ζ11−2ζ112ζ7−2ζ71−i3−1+i30000000000000000000000
χ894-4−4i4i000-240002-42i3−2i32i−2i−4i4i23−23-2000002i3−2i32002i−2i023−230000000000000000000000002-2−2i2i−1+i31−i3−2ζ72ζ7−2ζ112ζ11−1−i31+i30000000000000000000000
χ904-4−4i4i000-240002-42i3−2i32i−2i−4i4i23−23-2000002i3−2i32002i−2i023−23000000000000000000000000-222i−2i1−i3−1+i32ζ7−2ζ72ζ11−2ζ111+i3−1−i30000000000000000000000
χ918-88i−8i0008-4000-84008i−8i−4i4i00-40000000400−4i4i0000000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-400044−4i34i3−4i4i−4i4i43−432000002i3−2i3-2002i−2i0−23230000000000000000000000000000000000000000000000000000000000
χ938-88i−8i000-4-4000444i3−4i3−4i4i−4i4i−4343200000−2i32i3-2002i−2i023−230000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i0008-4000-8400−8i8i4i−4i00-400000004004i−4i0000000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-400044−4i34i34i−4i4i−4i−43432000002i3−2i3-200−2i2i023−230000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-4000444i3−4i34i−4i4i−4i43−43200000−2i32i3-200−2i2i0−23230000000000000000000000000000000000000000000000000000000000

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