Finite Group Databasebeta

← Group #11793992

Character table — Group #11793992

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222222444444444444444444448888888888888888888888242424242424242424242424242424242424242424242424363636367272
order12442223344466121212123666666666121212121212121212126688121224242424242424242424242424242424224444446666121212121212121212121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-111111111-1-1
χ922222222-12222-122-1-1-12-1-1-1-1-1-12222-1-1-1-12-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ1022222222-12222-122-1-1-12-1-1-1-1-1-12222-1-1-1-12-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ1122222222-12222-122-1-1-12-1-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-2-2-1-1-2-2-2-21111111111112-22-20000-1-111-1-11100000000000000
χ1222222222-12222-122-1-1-12-1-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-2-2-1-1-2-2-2-2111111111111-22-22000011-1-111-1-100000000000000
χ132222222-12222-12-1-122-1-1222-1-1-1-1-1-1-122-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ142222222-12222-12-1-122-1-1222-1-1-1-1-1-1-122-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ152222222-12222-12-1-122-1-1222-1-1-1-1-1-1-122-1-1-12-1-1-1-1-2-2-1-11111-2-2-2-211111111000022-2-200000000-1-1-1-11111000000
χ162222222-12222-12-1-122-1-1222-1-1-1-1-1-1-122-1-1-12-1-1-1-1-2-2-1-11111-2-2-2-2111111110000-2-222000000001111-1-1-1-1000000
χ1722222-2-2222-2-22222222-22-2-2-2-222-22-22-222-2-2-2-22-2002-200000000000000000000002i−2i0000000000002i2i−2i−2i000000
χ1822222-2-2222-2-22222222-22-2-2-2-222-22-22-222-2-2-2-22-2002-20000000000000000000000−2i2i000000000000−2i−2i2i2i000000
χ1922222-2-2-122-2-2-12-1-122-112-2-211-1-11-112-2-1-11-211-1100-1133−3−300003333−3−3−3−30000002i−2i00000000−i3−i3i3i3−i−iii000000
χ2022222-2-2-122-2-2-12-1-122-112-2-211-1-11-112-2-1-11-211-1100-1133−3−300003333−3−3−3−3000000−2i2i00000000i3i3−i3−i3ii−i−i000000
χ2122222-2-2-122-2-2-12-1-122-112-2-211-1-11-112-2-1-11-211-1100-11−3−3330000−3−3−3−333330000002i−2i00000000i3i3−i3−i3−i−iii000000
χ2222222-2-2-122-2-2-12-1-122-112-2-211-1-11-112-2-1-11-211-1100-11−3−3330000−3−3−3−33333000000−2i2i00000000−i3−i3i3i3ii−i−i000000
χ232222-22-222-22-22222222-2-22-2-2-22-22-22-2222-2-2-2-2-2200-22000000000000000000002i−2i00000000002i−2i2i−2i0000000000
χ242222-22-222-22-22222222-2-22-2-2-22-22-22-2222-2-2-2-2-2200-2200000000000000000000−2i2i0000000000−2i2i−2i2i0000000000
χ252222-22-2-12-22-2-12-1-122-11-22-211-11-11-1-22-1-11-2111-1001-13−33−3000033−3−333−3−300002i−2i0000000000−ii−ii−i3i3−i3i3000000
χ262222-22-2-12-22-2-12-1-122-11-22-211-11-11-1-22-1-11-2111-1001-13−33−3000033−3−333−3−30000−2i2i0000000000i−ii−ii3−i3i3−i3000000
χ272222-22-2-12-22-2-12-1-122-11-22-211-11-11-1-22-1-11-2111-1001-1−33−330000−3−333−3−33300002i−2i0000000000−ii−iii3−i3i3−i3000000
χ282222-22-2-12-22-2-12-1-122-11-22-211-11-11-1-22-1-11-2111-1001-1−33−330000−3−333−3−3330000−2i2i0000000000i−ii−i−i3i3−i3i3000000
χ292222-2-2222-2-2222222222-2-22222-2-2-2-2-2-2222222-2-22-2-2-22-2-2222-2-222-2-2-2-222000000000000000000000000000000
χ302222-2-2222-2-2222222222-2-22222-2-2-2-2-2-2222222-2-2-22-2-2-222-2-2-222-2-22222-2-2000000000000000000000000000000
χ312222-2-222-1-2-222-122-1-1-1211-1-1-1-1-2-2-2-211-1-12-1-1-1112-2112-2-22-1-111-1-11111-1-100000000−i3i3−i3i3−i3i3−i3i300000000000000
χ322222-2-222-1-2-222-122-1-1-1211-1-1-1-1-2-2-2-211-1-12-1-1-1112-2112-2-22-1-111-1-11111-1-100000000i3−i3i3−i3i3−i3i3−i300000000000000
χ332222-2-222-1-2-222-122-1-1-1211-1-1-1-1-2-2-2-211-1-12-1-1-111-2211-222-211-1-111-1-1-1-11100000000−i3i3i3−i3−i3i3i3−i300000000000000
χ342222-2-222-1-2-222-122-1-1-1211-1-1-1-1-2-2-2-211-1-12-1-1-111-2211-222-211-1-111-1-1-1-11100000000i3−i3−i3i3i3−i3−i3i300000000000000
χ352222-2-22-12-2-22-12-1-122-1-1-2-22-1-1-11111-2-2-1-1-12-1-1112-211-111-122-2-2-1-11111-1-100000000000000003−3−33−333−3000000
χ362222-2-22-12-2-22-12-1-122-1-1-2-22-1-1-11111-2-2-1-1-12-1-1112-211-111-122-2-2-1-11111-1-10000000000000000−333−33−3−33000000
χ372222-2-22-12-2-22-12-1-122-1-1-2-22-1-1-11111-2-2-1-1-12-1-111-22111-1-11-2-22211-1-1-1-11100000000000000003−3−333−3−33000000
χ382222-2-22-12-2-22-12-1-122-1-1-2-22-1-1-11111-2-2-1-1-12-1-111-22111-1-11-2-22211-1-1-1-1110000000000000000−333−3−333−3000000
χ3922-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22200-2-2000000000000000000000000000000000000000000002-2
χ4022-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22200-2-200000000000000000000000000000000000000000000-22
χ4122-2-22-2-222-22222-2-2-2-22-22-2-2-2-222-2-22-22-2-222222-200-22000000000000000020-2000002200-2-20000000000000000
χ4222-2-22-2-222-22222-2-2-2-22-22-2-2-2-222-2-22-22-2-222222-200-220000000000000000-20200000-2-200220000000000000000
χ4322-2-22-2-22-1-2222-1-2-211-1-2-11111-12-2-221-1112-1-1-1-11001-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i320-200000-1-1−i3i311i3−i300000000000000
χ4422-2-22-2-22-1-2222-1-2-211-1-2-11111-12-2-221-1112-1-1-1-11001-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-2020000011i3−i3-1-1−i3i300000000000000
χ4522-2-22-2-22-1-2222-1-2-211-1-2-11111-12-2-221-1112-1-1-1-11001-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i320-200000-1-1i3−i311−i3i300000000000000
χ4622-2-22-2-22-1-2222-1-2-211-1-2-11111-12-2-221-1112-1-1-1-11001-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-2020000011−i3i3-1-1i3−i300000000000000
χ4722-2-2-22-2222-2222-2-2-2-22-2-22-2-2-22-222-22-2-2-22222-22002-20000000000000000020-20000002200-2-200000000000000
χ4822-2-2-22-2222-2222-2-2-2-22-2-22-2-2-22-222-22-2-2-22222-22002-200000000000000000-202000000-2-2002200000000000000
χ4922-2-2-22-22-12-222-1-2-211-1-21-1111-1-222-2-11112-1-1-11-100-110000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3020-20000−i3i3-1-1i3−i31100000000000000
χ5022-2-2-22-22-12-222-1-2-211-1-21-1111-1-222-2-11112-1-1-11-100-110000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30-2020000i3−i311−i3i3-1-100000000000000
χ5122-2-2-22-22-12-222-1-2-211-1-21-1111-1-222-2-11112-1-1-11-100-110000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3020-20000i3−i3-1-1−i3i31100000000000000
χ5222-2-2-22-22-12-222-1-2-211-1-21-1111-1-222-2-11112-1-1-11-100-110000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30-2020000−i3i311i3−i3-1-100000000000000
χ5322-2-2-2-222222-222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2-2-2002200000000000000000000000000000000000000002i2i−2i−2i00
χ5422-2-2-2-222222-222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2-2-200220000000000000000000000000000000000000000−2i−2i2i2i00
χ554444444-2-2444-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-2-211-2-211114411-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ564444444-2-2444-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-2-211-2-21111-4-41122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5744444-4-44-24-4-44-244-2-2-2-4-22222-24-44-4-22-2-2-4222-2200-220000000000000000000000000000000000000000000000
χ5844444-4-4-2-24-4-4-2-2-2-2-2-212-222-1-11-22-22-221122-1-11-1001-12323−23−230000−3−3−3−33333000000000000000000000000000000
χ5944444-4-4-2-24-4-4-2-2-2-2-2-212-222-1-11-22-22-221122-1-11-1001-1−23−23232300003333−3−3−3−3000000000000000000000000000000
χ604444-44-44-2-44-44-244-2-2-2-42-2222-2-44-442-2-2-2-42222-2002-20000000000000000000000000000000000000000000000
χ614444-44-4-2-2-44-4-2-2-2-2-2-2122-22-1-112-22-22-21122-1-1-1100-1123−2323−230000−3−333−3−333000000000000000000000000000000
χ624444-44-4-2-2-44-4-2-2-2-2-2-2122-22-1-112-22-22-21122-1-1-1100-11−2323−2323000033−3−333−3−3000000000000000000000000000000
χ634444-4-44-2-2-4-44-2-2-2-2-2-21-222-211122222211-2-211-1-14-4-1-1-222-2-2-22211-1-1-1-111000000000000000000000000000000
χ644444-4-44-2-2-4-44-2-2-2-2-2-21-222-211122222211-2-211-1-1-44-1-12-2-2222-2-2-1-11111-1-1000000000000000000000000000000
χ6544-4-44444-2-4-4-44-2-4-422-24-2-2-2-2-2-244-4-42222-4222-2-200220000000000000000000000000000000000000000000000
χ6644-4-4444-24-4-4-4-2422-4-4-2-2444-2-2-2-2-222-4-4222-422-2-200220000000000000000000000000000000000000000000000
χ6744-4-4444-2-2-4-4-4-2-222221-2-2-2-2111-2-22222-1-122-1-11100-1-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000
χ6844-4-4444-2-2-4-4-4-2-222221-2-2-2-2111-2-22222-1-122-1-11100-1-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000
χ6944-4-44-4-4-24-444-2422-4-4-224-4-422-2-222-2-4422-24-2-2-22002-20000000000000000000000000000000000000000000000
χ7044-4-44-4-4-2-2-444-2-2222212-222-1-11-222-22-2-1-1-2-2111-100-110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000
χ7144-4-44-4-4-2-2-444-2-2222212-222-1-11-222-22-2-1-1-2-2111-100-1100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000
χ7244-4-4-44-4-244-44-2422-4-4-22-44-422-22-2-224-422-24-2-22-200-220000000000000000000000000000000000000000000000
χ7344-4-4-44-4-2-24-44-2-22222122-22-1-112-2-22-22-1-1-2-211-11001-10000−2i32i32i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000
χ7444-4-4-44-4-2-24-44-2-22222122-22-1-112-2-22-22-1-1-2-211-11001-100002i3−2i3−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000
χ7544-4-4-4-444-244-44-2-4-422-2422-2-2-2-2-4-444-2-222-42222200-2-20000000000000000000000000000000000000000000000
χ7644-4-4-4-44-2444-4-2422-4-4-2-2-4-44-2-2-222-2-244222-4222200-2-20000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-244-4-2-222221-222-211122-2-2-2-2-1-122-1-1-1-10011000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000
χ7844-4-4-4-44-2-244-4-2-222221-222-211122-2-2-2-2-1-122-1-1-1-1001100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000
χ794-44i−4i00044000-4-44i−4i4i−4i4000000-40000004i−4i000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ804-44i−4i00044000-4-44i−4i4i−4i4000000-40000004i−4i00000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ814-4−4i4i00044000-4-4−4i4i−4i4i4000000-4000000−4i4i00000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ824-4−4i4i00044000-4-4−4i4i−4i4i4000000-4000000−4i4i000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ838-88i−8i0008-4000-848i−8i−4i4i-40000004000000−4i4i00000000000000000000000000000000000000000000000000000000
χ848-88i−8i000-480004-8−4i4i8i−8i-40000004000000−4i4i00000000000000000000000000000000000000000000000000000000
χ858-88i−8i000-4-400044−4i4i−4i4i200006-6-20000002i−2i006i−6i0000000000000000000000000000000000000000000000000000
χ868-88i−8i000-4-400044−4i4i−4i4i20000-66-20000002i−2i00−6i6i0000000000000000000000000000000000000000000000000000
χ878-8−8i8i0008-4000-84−8i8i4i−4i-400000040000004i−4i00000000000000000000000000000000000000000000000000000000
χ888-8−8i8i000-480004-84i−4i−8i8i-400000040000004i−4i00000000000000000000000000000000000000000000000000000000
χ898-8−8i8i000-4-4000444i−4i4i−4i200006-6-2000000−2i2i00−6i6i0000000000000000000000000000000000000000000000000000
χ908-8−8i8i000-4-4000444i−4i4i−4i20000-66-2000000−2i2i006i−6i0000000000000000000000000000000000000000000000000000

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