Finite Group Databasebeta

← Group #13147282

Character table — Group #13147282

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222222666666666666121212121212121212121212121212121212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order12222236666666344446666666336666661212121212121212121212121212121244443366666666666666666644441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ411111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32
χ511111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ611111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32
χ71111-1-1111-1-1-1-11111-1-111-1-1-1-111111111111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1
χ81111-1-1111-1-1-1-11111-1-111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-111-1-111
χ91111-1-1111-1-1-1-11111-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1111111-1-1-1-1-1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ101111-1-1111-1-1-1-11111-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1111111-1-1-1-1-1-1-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ111111-1-1111-1-1-1-11111-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1111111-1-1-1-1-1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ121111-1-1111-1-1-1-11111-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1111111-1-1-1-1-1-1-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-11-11-1-111-1-1111-11-1-1-111-1-111111-1-1-1-11-11-1111-1-1-1111-1-1-1i−ii−i111-11-11-1-111-1-11-1-111-1-1i−ii−ii−ii−ii−ii−i
χ1411-1-11-11-1-111-1-1111-11-1-1-111-1-111111-1-1-1-11-11-1111-1-1-1111-1-1-1−ii−ii111-11-11-1-111-1-11-1-111-1-1−ii−ii−ii−ii−ii−ii
χ1511-1-11-11-1-111-1-1111-11-1-1-111-1-11−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-11-1111-1-1-1111-1-1-1i−ii−i−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32i−ii−iζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ1611-1-11-11-1-111-1-1111-11-1-1-111-1-11−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-11-1111-1-1-1111-1-1-1−ii−ii−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ii−ii−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ1711-1-11-11-1-111-1-1111-11-1-1-111-1-11−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-11-1111-1-1-1111-1-1-1i−ii−i−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32i−ii−iζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ1811-1-11-11-1-111-1-1111-11-1-1-111-1-11−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-11-1111-1-1-1111-1-1-1−ii−ii−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ii−ii−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ1911-1-1-111-1-1-1-111111-1-11-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1111i−i−ii11-11-111-1-1-1-1111-1-1-1-111i−i−iii−i−iii−i−ii
χ2011-1-1-111-1-1-1-111111-1-11-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1111−iii−i11-11-111-1-1-1-1111-1-1-1-111−iii−i−iii−i−iii−i
χ2111-1-1-111-1-1-1-111111-1-11-1-1-1-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-11111-1-1-1-1-1-1111i−i−ii−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32i−i−iiζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ2211-1-1-111-1-1-1-111111-1-11-1-1-1-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-11111-1-1-1-1-1-1111−iii−i−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−iii−i−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ2311-1-1-111-1-1-1-111111-1-11-1-1-1-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-11111-1-1-1-1-1-1111i−i−ii−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32i−i−iiζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ2411-1-1-111-1-1-1-111111-1-11-1-1-1-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-11111-1-1-1-1-1-1111−iii−i−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−iii−i−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ2522222222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2622222222222222-12222-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-100001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i32000000000000
χ2722222222222222-12222-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-100001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i32000000000000
χ282222-2-2222-2-2-2-22-122-2-2-1-11111-12222222222-2-2-1-1-1-1-1-11111110000-1-1-2-2-2-2-1-1-11111-1-1-11111000000000000
χ292222-2-2222-2-2-2-22-122-2-2-1-11111-1−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322-2-2-1-1-1-1-1-111111100001+i321−i321+i31+i31−i31−i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ302222-2-2222-2-2-2-22-122-2-2-1-11111-1−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322-2-2-1-1-1-1-1-111111100001−i321+i321−i31−i31+i31+i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3122-2-22-22-2-222-2-22-12-22-211-1-111-12222-2-2-2-22-22-2-1-1-1111-1-1-11110000-1-12-22-2-111-1-111-111-1-111000000000000
χ3222-2-22-22-2-222-2-22-12-22-211-1-111-1−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i32-22-2-1-1-1111-1-1-111100001+i321−i32−1−i31+i3−1+i31−i31+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32000000000000
χ3322-2-22-22-2-222-2-22-12-22-211-1-111-1−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i32-22-2-1-1-1111-1-1-111100001−i321+i32−1+i31−i3−1−i31+i31−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32000000000000
χ3422-2-2-222-2-2-2-2222-12-2-221111-1-1-12222-2-2-2-22-2-22-1-1-1111111-1-1-10000-1-1-22-22-11111-1-1-11111-1-1000000000000
χ3522-2-2-222-2-2-2-2222-12-2-221111-1-1-1−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i32-2-22-1-1-1111111-1-1-100001+i321−i321+i3−1−i31−i3−1+i31+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32000000000000
χ3622-2-2-222-2-2-2-2222-12-2-221111-1-1-1−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i32-2-22-1-1-1111111-1-1-100001−i321+i321−i3−1+i31+i3−1−i31−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32000000000000
χ37333333333333333-1-1-1-1333333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333300000000000000000000-1-1-1-100000000
χ38333333333333333-1-1-1-1333333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000000000000000111100000000
χ393333-3-3333-3-3-3-333-1-11133-3-3-3-3300000000-1-111-1-1-1-1-1-111111133-3-300000000000000000000-1-11100000000
χ403333-3-3333-3-3-3-333-1-11133-3-3-3-3300000000-1-111-1-1-1-1-1-1111111-3-3330000000000000000000011-1-100000000
χ4133-3-33-33-3-333-3-333-11-11-3-333-3-3300000000-11-11-1-1-1111-1-1-11113i−3i3i−3i00000000000000000000−ii−ii00000000
χ4233-3-33-33-3-333-3-333-11-11-3-333-3-3300000000-11-11-1-1-1111-1-1-1111−3i3i−3i3i00000000000000000000i−ii−i00000000
χ4333-3-3-333-3-3-3-33333-111-1-3-3-3-333300000000-111-1-1-1-1111111-1-1-13i−3i−3i3i00000000000000000000−iii−i00000000
χ4433-3-3-333-3-3-3-33333-111-1-3-3-3-333300000000-111-1-1-1-1111111-1-1-1−3i3i3i−3i00000000000000000000i−i−ii00000000
χ454-44-40044-40000-4400004-40000-4-2-2222-22-200000000000000000000-2-2000022-2000022-20000000000000000
χ464-44-40044-40000-4400004-40000-41+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000001+i31−i30000−1−i3−1−i31+i30000−1+i3−1+i31−i30000000000000000
χ474-44-40044-40000-4400004-40000-41−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000001−i31+i30000−1+i3−1+i31−i30000−1−i3−1−i31+i30000000000000000
χ484-44-40044-40000-4-20000-22−2i32i3−2i32i32-2-2222-22-200000000000000000000110000-1-11−i3i3−i3i3-1-11−i3i3−i3i3000000000000
χ494-44-40044-40000-4-20000-22−2i32i3−2i32i321+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000−1−i32−1+i3200001+i321+i32−1−i32−3+i323−i32−3+i323−i321−i321−i32−1+i323+i32−3−i323+i32−3−i32000000000000
χ504-44-40044-40000-4-20000-22−2i32i3−2i32i321−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000−1+i32−1−i3200001−i321−i32−1+i323+i32−3−i323+i32−3−i321+i321+i32−1−i32−3+i323−i32−3+i323−i32000000000000
χ514-44-40044-40000-4-20000-222i3−2i32i3−2i32-2-2222-22-200000000000000000000110000-1-11i3−i3i3−i3-1-11i3−i3i3−i3000000000000
χ524-44-40044-40000-4-20000-222i3−2i32i3−2i321+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000−1−i32−1+i3200001+i321+i32−1−i323−i32−3+i323−i32−3+i321−i321−i32−1+i32−3−i323+i32−3−i323+i32000000000000
χ534-44-40044-40000-4-20000-222i3−2i32i3−2i321−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000−1+i32−1−i3200001−i321−i32−1+i32−3−i323+i32−3−i323+i321+i321+i32−1−i323−i32−3+i323−i32−3+i32000000000000
χ544-4-44004-440000-440000-440000-4-2-222-22-2200000000000000000000-2-200002-2200002-220000000000000000
χ554-4-44004-440000-440000-440000-41+i31−i3−1−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000001+i31−i30000−1−i31+i3−1−i30000−1+i31−i3−1+i30000000000000000
χ564-4-44004-440000-440000-440000-41−i31+i3−1+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000001−i31+i30000−1+i31−i3−1+i30000−1−i31+i3−1−i30000000000000000
χ574-4-44004-440000-4-200002-2−2i32i32i3−2i32-2-222-22-2200000000000000000000110000-11-1−i3i3i3−i3-11-1−i3i3i3−i3000000000000
χ584-4-44004-440000-4-200002-2−2i32i32i3−2i321+i31−i3−1−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000−1−i32−1+i3200001+i32−1−i321+i32−3+i323−i323−i32−3+i321−i32−1+i321−i323+i32−3−i32−3−i323+i32000000000000
χ594-4-44004-440000-4-200002-2−2i32i32i3−2i321−i31+i3−1+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000−1+i32−1−i3200001−i32−1+i321−i323+i32−3−i32−3−i323+i321+i32−1−i321+i32−3+i323−i323−i32−3+i32000000000000
χ604-4-44004-440000-4-200002-22i3−2i3−2i32i32-2-222-22-2200000000000000000000110000-11-1i3−i3−i3i3-11-1i3−i3−i3i3000000000000
χ614-4-44004-440000-4-200002-22i3−2i3−2i32i321+i31−i3−1−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000−1−i32−1+i3200001+i32−1−i321+i323−i32−3+i32−3+i323−i321−i32−1+i321−i32−3−i323+i323+i32−3−i32000000000000
χ624-4-44004-440000-4-200002-22i3−2i3−2i32i321−i31+i3−1+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000−1+i32−1−i3200001−i32−1+i321−i32−3−i323+i323+i32−3−i321+i32−1−i321+i323−i32−3+i32−3+i323−i32000000000000
χ6366666666666666-3-2-2-2-2-3-3-3-3-3-3-300000000-2-2-2-2111111111111000000000000000000000000000000000000
χ64666666-3-3-3-3-3-3-3-306666000000000000000-3-3-3-3000000000000000000000000000000000000000000000000
χ65666666-3-3-3-3-3-3-3-30-2-2-2-200000000000000011114-2-24-2-24-2-24-2-2000000000000000000000000000000000000
χ66666666-3-3-3-3-3-3-3-30-2-2-2-20000000000000001111-24-2-24-2-24-2-24-2000000000000000000000000000000000000
χ67666666-3-3-3-3-3-3-3-30-2-2-2-20000000000000001111-2-24-2-24-2-24-2-24000000000000000000000000000000000000
χ686666-6-6666-6-6-6-66-3-2-222-3-33333-300000000-2-222111111-1-1-1-1-1-1000000000000000000000000000000000000
χ696666-6-6-3-3-33333-3066-6-6000000000000000-3-333000000000000000000000000000000000000000000000000
χ706666-6-6-3-3-33333-30-2-22200000000000000011-1-14-2-24-2-2-422-422000000000000000000000000000000000000
χ716666-6-6-3-3-33333-30-2-22200000000000000011-1-1-24-2-24-22-422-42000000000000000000000000000000000000
χ726666-6-6-3-3-33333-30-2-22200000000000000011-1-1-2-24-2-2422-422-4000000000000000000000000000000000000
χ7366-6-66-66-6-666-6-66-3-22-2233-3-333-300000000-22-22111-1-1-1111-1-1-1000000000000000000000000000000000000
χ7466-6-66-6-333-3-333-306-66-6000000000000000-33-33000000000000000000000000000000000000000000000000
χ7566-6-66-6-333-3-333-30-22-220000000000000001-11-14-2-2-4224-2-2-422000000000000000000000000000000000000
χ7666-6-66-6-333-3-333-30-22-220000000000000001-11-1-24-22-42-24-22-42000000000000000000000000000000000000
χ7766-6-66-6-333-3-333-30-22-220000000000000001-11-1-2-2422-4-2-2422-4000000000000000000000000000000000000
χ7866-6-6-666-6-6-6-6666-3-222-23333-3-3-300000000-222-2111-1-1-1-1-1-1111000000000000000000000000000000000000
χ7966-6-6-66-33333-3-3-306-6-66000000000000000-333-3000000000000000000000000000000000000000000000000
χ8066-6-6-66-33333-3-3-30-222-20000000000000001-1-114-2-2-422-4224-2-2000000000000000000000000000000000000
χ8166-6-6-66-33333-3-3-30-222-20000000000000001-1-11-24-22-422-42-24-2000000000000000000000000000000000000
χ8266-6-6-66-33333-3-3-30-222-20000000000000001-1-11-2-2422-422-4-2-24000000000000000000000000000000000000
χ8312-1212-1200-6-66−6i36i3−6i36i36000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-1200-6-666i3−6i36i3−6i36000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-121200-66-6−6i36i36i3−6i36000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-121200-66-66i3−6i3−6i36i36000000000000000000000000000000000000000000000000000000000000000000000000

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