Finite Group Databasebeta

← Group #13136957

Character table — Group #13136957

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111112224444444441212121212121212121212121212121212121212121212121212121212121212363636363636727272727272727272727272727272
order12336626622266666633666666666666666666666666666666246612124448812121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1i−ii−i-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1−ii−ii-1-1−i−iii−i−iii
χ51111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-1
χ61111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11i−i−ii11ii−i−i−i−iii
χ81111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−iii−i11−i−iiiii−i−i
χ9222222222-200-2-2000022222222-2-2-2-2-2-2-2-200000000000000002-222-2-2000000000000000
χ10222222222-200-2-2000022222222-2-2-2-2-2-2-2-20000000000000000-22-2-222000000000000000
χ1133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i320000000000000000000000000000000011−1−i32−1+i32−1−i32−1+i321i−ii−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11ζ7ζ11−ζ7−ζ11
χ1233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i320000000000000000000000000000000011−1−i32−1+i32−1−i32−1+i321−ii−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11−ζ7−ζ11ζ7ζ11
χ1333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000000000000000000000-1-11+i321−i321+i321−i32-111111+i321−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ1433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000000000000000000000-1-11+i321−i321+i321−i32-1-1-1-1-11+i321−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ1533−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i320000000000000000000000000000000011−1−i32−1+i32−1−i32−1+i32-1i−i−ii1+i321−i32ζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11
χ1633−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i320000000000000000000000000000000011−1−i32−1+i32−1−i32−1+i32-1−iii−i1+i321−i32−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11
χ1733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i3200000000000000000000000000000000-1-11+i321−i321+i321−i32111-1-1−1−i32−1+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ1833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i3200000000000000000000000000000000-1-11+i321−i321+i321−i321-1-111−1−i32−1+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ1933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i320000000000000000000000000000000011−1+i32−1−i32−1+i32−1−i321i−ii−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7
χ2033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i320000000000000000000000000000000011−1+i32−1−i32−1+i32−1−i321−ii−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7
χ2133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000000000000000000000-1-11−i321+i321−i321+i32-111111−i321+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000000000000000000000-1-11−i321+i321−i321+i32-1-1-1-1-11−i321+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ2333−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i320000000000000000000000000000000011−1+i32−1−i32−1+i32−1−i32-1i−i−ii1−i321+i32ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ2433−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i320000000000000000000000000000000011−1+i32−1−i32−1+i32−1−i32-1−iii−i1−i321+i32−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ2533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i3200000000000000000000000000000000-1-11−i321+i321−i321+i32111-1-1−1+i32−1−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ2633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i3200000000000000000000000000000000-1-11−i321+i321−i321+i321-1-111−1+i32−1−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ274444444444444444441-2111-2-2-21111-2-2-2-211111111-2-2-2-2-2-2-2-2000000000000000000000
χ28444444444444444444-21-2-2-2111-2-2-2-21111-2-2-2-2-2-2-2-211111111000000000000000000000
χ294444444444-4-444-4-4-4-41-2111-2-2-21111-2-2-2-2-1-1-1-1-1-1-1-122222222000000000000000000000
χ304444444444-4-444-4-4-4-4-21-2-2-2111-2-2-2-2111122222222-1-1-1-1-1-1-1-1000000000000000000000
χ31444444444-400-4-400001-2111-2-2-2-1-1-1-122223333-3-3-3-300000000000000000000000000000
χ32444444444-400-4-400001-2111-2-2-2-1-1-1-12222-3-3-3-3333300000000000000000000000000000
χ33444444444-400-4-40000-21-2-2-21112222-1-1-1-1000000003333-3-3-3-3000000000000000000000
χ34444444444-400-4-40000-21-2-2-21112222-1-1-1-100000000-3-3-3-33333000000000000000000000
χ35444444-4-4-40000000001-21-1-122-233-3-30000−i3−i3i3i3−i3−i3i3i30000−2i3−2i32i32i3000000000000000000000
χ36444444-4-4-40000000001-21-1-122-233-3-30000i3i3−i3−i3i3i3−i3−i300002i32i3−2i3−2i3000000000000000000000
χ37444444-4-4-40000000001-21-1-122-2-3-3330000−i3−i3i3i3i3i3−i3−i3−2i3−2i32i32i30000000000000000000000000
χ38444444-4-4-40000000001-21-1-122-2-3-3330000i3i3−i3−i3−i3−i3i3i32i32i3−2i3−2i30000000000000000000000000
χ39444444-4-4-4000000000444-4-4-4-44000000000000000000000000000000000000000000000
χ40444444-4-4-4000000000-21-222-1-11000033-3-30000−2i3−2i32i32i3−i3−i3i3i3i3i3−i3−i3000000000000000000000
χ41444444-4-4-4000000000-21-222-1-11000033-3-300002i32i3−2i3−2i3i3i3−i3−i3−i3−i3i3i3000000000000000000000
χ42444444-4-4-4000000000-21-222-1-110000-3-333−2i3−2i32i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000
χ43444444-4-4-4000000000-21-222-1-110000-3-3332i32i3−2i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000
χ444-444-4-400002-2002-22-21-2-13-3002−i3i3−i3i300−2i32i31-11-12+i3−2−i32−i3−2+i31+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i3000000000000000000000
χ454-444-4-400002-2002-22-21-2-13-3002i3−i3i3−i3002i3−2i31-11-12−i3−2+i32+i3−2−i31−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i3000000000000000000000
χ464-444-4-400002-2002-22-21-2-1-33002−i3i3i3−i3−2i32i300−2+i32−i3−2−i32+i3-11-111+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000
χ474-444-4-400002-2002-22-21-2-1-33002i3−i3−i3i32i3−2i300−2−i32+i3−2+i32−i3-11-111−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000
χ484-444-4-400002-2002-22-244-40000-400000000-22-222-22-2-22-22-22-22000000000000000000000
χ494-444-4-400002-2002-22-2-212003-3-100−2i32i3−i3i3i3−i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i31-11-1−2+i32−i3−2−i32+i3000000000000000000000
χ504-444-4-400002-2002-22-2-212003-3-1002i3−2i3i3−i3−i3i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i31-11-1−2−i32+i3−2+i32−i3000000000000000000000
χ514-444-4-400002-2002-22-2-21200-33-1−2i32i300i3−i3i3−i31+i3−1−i31−i3−1+i3−1+i31−i3−1−i31+i3−2−i32+i3−2+i32−i31-11-1000000000000000000000
χ524-444-4-400002-2002-22-2-21200-33-12i3−2i300−i3i3−i3i31−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i3−2+i32−i3−2−i32+i31-11-1000000000000000000000
χ534-444-4-40000-2200-22-221-2-13-3002−i3i3−i3i300−2i32i3-11-11−2−i32+i3−2+i32−i3−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3000000000000000000000
χ544-444-4-40000-2200-22-221-2-13-3002i3−i3i3−i3002i3−2i3-11-11−2+i32−i3−2−i32+i3−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3000000000000000000000
χ554-444-4-40000-2200-22-221-2-1-33002−i3i3i3−i3−2i32i3002−i3−2+i32+i3−2−i31-11-1−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000
χ564-444-4-40000-2200-22-221-2-1-33002i3−i3−i3i32i3−2i3002+i3−2−i32−i3−2+i31-11-1−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000
χ574-444-4-40000-2200-22-2244-40000-4000000002-22-2-22-222-22-22-22-2000000000000000000000
χ584-444-4-40000-2200-22-22-212003-3-100−2i32i3−i3i3i3−i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3-11-112−i3−2+i32+i3−2−i3000000000000000000000
χ594-444-4-40000-2200-22-22-212003-3-1002i3−2i3i3−i3−i3i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3-11-112+i3−2−i32−i3−2+i3000000000000000000000
χ604-444-4-40000-2200-22-22-21200-33-1−2i32i300i3−i3i3−i3−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i32+i3−2−i32−i3−2+i3-11-11000000000000000000000
χ614-444-4-40000-2200-22-22-21200-33-12i3−2i300−i3i3−i3i3−1+i31−i3−1−i31+i31+i3−1−i31−i3−1+i32−i3−2+i32+i3−2−i3-11-11000000000000000000000
χ6266−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-6003+3i33−3i30000000000000000000000000000000000002-2−1−i3−1+i31+i31−i3000000000000000
χ6366−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-6003+3i33−3i3000000000000000000000000000000000000-221+i31−i3−1−i3−1+i3000000000000000
χ6466−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-6003−3i33+3i30000000000000000000000000000000000002-2−1+i3−1−i31−i31+i3000000000000000
χ6566−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-6003−3i33+3i3000000000000000000000000000000000000-221−i31+i3−1+i3−1−i3000000000000000
χ661212−6−6i3−6+6i3−6−6i3−6+6i3-126+6i36−6i300000000000000000000000000000000000000000000000000000000000000
χ671212−6+6i3−6−6i3−6+6i3−6−6i3-126−6i36+6i300000000000000000000000000000000000000000000000000000000000000
χ6812-12−6−6i3−6+6i36+6i36−6i300006-600−3−3i33+3i3−3+3i33−3i300000000000000000000000000000000000000000000000000000
χ6912-12−6−6i3−6+6i36+6i36−6i30000-66003+3i3−3−3i33−3i3−3+3i300000000000000000000000000000000000000000000000000000
χ7012-12−6+6i3−6−6i36−6i36+6i300006-600−3+3i33−3i3−3−3i33+3i300000000000000000000000000000000000000000000000000000
χ7112-12−6+6i3−6−6i36−6i36+6i30000-66003−3i3−3+3i33+3i3−3−3i300000000000000000000000000000000000000000000000000000

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