Finite Group Databasebeta

← Group #13147032

Character table — Group #13147032

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111122222222266666666666666121212121212121212121212121212242424242424242424242424242424242424242424242424727272727272727272727272
order123366488121224242424234666121212122424242466681212122424242424242424333666121212121212242424242424242424242424246688121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111-1-111-1-1-1-11111111111-1-1-1-1111-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-1
χ41111111-1-111-1-1-1-11111111111-1-1-1-1111-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111
χ522222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ62222222222222222-1222-1-1-122-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ72222222222222222-1222-1-1-122-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-12-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1000000000000
χ82222222222222222-1222-1-1-122-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-12222000000000000
χ92222222-2-222-2-2-2-22222222222-2-2-2-2222-2222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000
χ102222222-2-222-2-2-2-22-1222-1-1-1221111-1-1-1-2-1-1-1-2-21111112-1-12-1-122-1-1-1-1-2-2-2-211111111000000000000
χ112222222-2-222-2-2-2-22-1222-1-1-1221111-1-1-1-2-1-1-1-2-2111111-12-1-12-1-1-122-1-11111-2-2-2-21111000000000000
χ122222222-2-222-2-2-2-22-1222-1-1-1221111-1-1-1-2-1-1-1-2-2111111-1-12-1-12-1-1-1-12211111111-2-2-2-2000000000000
χ13222222-200-2-20000-222-2-22-2-2220000-2-2-2022200000000222222-2-2-2-2-2-2000000000000000000000000
χ14222222-200-2-20000-222-2-22-2-2220000-2-2-2022200000000-1-1-1-1-1-111111133−3−333−3−333−3−3000000000000
χ15222222-200-2-20000-222-2-22-2-2220000-2-2-2022200000000-1-1-1-1-1-1111111−3−333−3−333−3−333000000000000
χ16222222-200-2-20000-2-12-2-2-1112233−3−31110-1-1-100333−3−3−32-1-12-1-1-2-21111000033−3−3−3−333000000000000
χ17222222-200-2-20000-2-12-2-2-1112233−3−31110-1-1-100333−3−3−3-12-1-12-111-2-211−3−333000033−3−3000000000000
χ18222222-200-2-20000-2-12-2-2-1112233−3−31110-1-1-100333−3−3−3-1-12-1-121111-2-233−3−3−3−3330000000000000000
χ19222222-200-2-20000-2-12-2-2-11122−3−3331110-1-1-100−3−3−33332-1-12-1-1-2-211110000−3−33333−3−3000000000000
χ20222222-200-2-20000-2-12-2-2-11122−3−3331110-1-1-100−3−3−3333-12-1-12-111-2-21133−3−30000−3−333000000000000
χ21222222-200-2-20000-2-12-2-2-11122−3−3331110-1-1-100−3−3−3333-1-12-1-121111-2-2−3−33333−3−30000000000000000
χ22333333333333333-13-1-1-1333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000001111-1-111-1-1-1-1
χ23333333333333333-13-1-1-1333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-111-1-11111
χ243333333-3-333-3-3-3-3-13-1-1-1333-1-1-3-3-3-3-1-1-11-1-1-1111111110000000000000000000000001-111-11-1-1-1-111
χ253333333-3-333-3-3-3-3-13-1-1-1333-1-1-3-3-3-3-1-1-11-1-1-111111111000000000000000000000000-11-1-11-11111-1-1
χ2633−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i3200000003000−3−3i32−3+3i3200000000000000000000000000000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i3200000003000−3−3i32−3+3i32000000000000000000000000000000-1-11+i321−i32-1-11+i321−i321+i321−i321+i321−i32
χ2833−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-10-11+i321−i320001+i321−i3200002−1−i3−1+i3-12−1−i3−1+i31+i321−i322−1−i3−1+i32−1−i3−1+i300000000000000000000000011−1−i32−1+i32-1-1−1−i32−1+i321+i321−i321+i321−i32
χ2933−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-10-11+i321−i320001+i321−i3200002−1−i3−1+i3-12−1−i3−1+i31+i321−i322−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-11+i321−i32111+i321−i32−1−i32−1+i32−1−i32−1+i32
χ3033−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32303−3−3i32−3+3i32000−3−3i32−3+3i320000000-30003+3i323−3i320000000000000000000000000000001-1−1−i32−1+i321-11+i321−i32−1−i32−1+i321+i321−i32
χ3133−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32303−3−3i32−3+3i32000−3−3i32−3+3i320000000-30003+3i323−3i32000000000000000000000000000000-111+i321−i32-11−1−i32−1+i321+i321−i32−1−i32−1+i32
χ3233−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-10-11+i321−i320001+i321−i3200002−1−i3−1+i312−1−i3−1+i3−1−i32−1+i32-21+i31−i3-21+i31−i30000000000000000000000001-1−1−i32−1+i32-111+i321−i321+i321−i32−1−i32−1+i32
χ3333−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-10-11+i321−i320001+i321−i3200002−1−i3−1+i312−1−i3−1+i3−1−i32−1+i32-21+i31−i3-21+i31−i3000000000000000000000000-111+i321−i321-1−1−i32−1+i32−1−i32−1+i321+i321−i32
χ3433−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i3200000003000−3+3i32−3−3i3200000000000000000000000000000011−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ3533−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i3200000003000−3+3i32−3−3i32000000000000000000000000000000-1-11−i321+i32-1-11−i321+i321−i321+i321−i321+i32
χ3633−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-10-11−i321+i320001−i321+i3200002−1+i3−1−i3-12−1+i3−1−i31−i321+i322−1+i3−1−i32−1+i3−1−i300000000000000000000000011−1+i32−1−i32-1-1−1+i32−1−i321−i321+i321−i321+i32
χ3733−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-10-11−i321+i320001−i321+i3200002−1+i3−1−i3-12−1+i3−1−i31−i321+i322−1+i3−1−i32−1+i3−1−i3000000000000000000000000-1-11−i321+i32111−i321+i32−1+i32−1−i32−1+i32−1−i32
χ3833−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32303−3+3i32−3−3i32000−3+3i32−3−3i320000000-30003−3i323+3i320000000000000000000000000000001-1−1+i32−1−i321-11−i321+i32−1+i32−1−i321−i321+i32
χ3933−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32303−3+3i32−3−3i32000−3+3i32−3−3i320000000-30003−3i323+3i32000000000000000000000000000000-111−i321+i32-11−1+i32−1−i321−i321+i32−1+i32−1−i32
χ4033−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32-10-11−i321+i320001−i321+i3200002−1+i3−1−i312−1+i3−1−i3−1+i32−1−i32-21−i31+i3-21−i31+i30000000000000000000000001-1−1+i32−1−i32-111−i321+i321−i321+i32−1+i32−1−i32
χ4133−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32-10-11−i321+i320001−i321+i3200002−1+i3−1−i312−1+i3−1−i3−1+i32−1−i32-21−i31+i3-21−i31+i3000000000000000000000000-111−i321+i321-1−1+i32−1−i32−1+i32−1−i321−i321+i32
χ424-444-4-40−2i22i200−2i22i2−2i22i204000-40000−2i22i2−2i22i2000000000000000111-1-1-13−33−33−3ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ434-444-4-40−2i22i200−2i22i2−2i22i204000-40000−2i22i2−2i22i2000000000000000111-1-1-1−33−33−33ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ444-444-4-40−2i22i200−2i22i2−2i22i204000-40000−2i22i2−2i22i2000000000000000-2-2-2222000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ454-444-4-40−2i22i200−2i22i2−2i22i20-2000223−23002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000011-2-1-123−3−3300ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−i2i2i2−i2000000000000
χ464-444-4-40−2i22i200−2i22i2−2i22i20-2000223−23002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ230000000000000001-21-12-1−33003−3ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−i2i2i2−i2ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ474-444-4-40−2i22i200−2i22i2−2i22i20-2000223−23002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000-2112-1-1003−3−33−i2i2i2−i2ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ484-444-4-40−2i22i200−2i22i2−2i22i20-20002−2323002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000011-2-1-12−333−300ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−i2i2i2−i2000000000000
χ494-444-4-40−2i22i200−2i22i2−2i22i20-20002−2323002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000001-21-12-13−300−33ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−i2i2i2−i2ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ504-444-4-40−2i22i200−2i22i2−2i22i20-20002−2323002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000-2112-1-100−333−3−i2i2i2−i2ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ514-444-4-402i2−2i2002i2−2i22i2−2i204000-400002i2−2i22i2−2i2000000000000000111-1-1-13−33−33−3−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ524-444-4-402i2−2i2002i2−2i22i2−2i204000-400002i2−2i22i2−2i2000000000000000111-1-1-1−33−33−33−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ534-444-4-402i2−2i2002i2−2i22i2−2i204000-400002i2−2i22i2−2i2000000000000000-2-2-2222000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ544-444-4-402i2−2i2002i2−2i22i2−2i20-2000223−2300−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000011-2-1-123−3−3300−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7i2−i2−i2i2000000000000
χ554-444-4-402i2−2i2002i2−2i22i2−2i20-2000223−2300−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ230000000000000001-21-12-1−33003−3−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7i2−i2−i2i2−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ564-444-4-402i2−2i2002i2−2i22i2−2i20-2000223−2300−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000-2112-1-1003−3−33i2−i2−i2i2−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ574-444-4-402i2−2i2002i2−2i22i2−2i20-20002−232300−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000011-2-1-12−333−300−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23i2−i2−i2i2000000000000
χ584-444-4-402i2−2i2002i2−2i22i2−2i20-20002−232300−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000001-21-12-13−300−33−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23i2−i2−i2i2−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ594-444-4-402i2−2i2002i2−2i22i2−2i20-20002−232300−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000-2112-1-100−333−3i2−i2−i2i2−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ60666666666666666-2-3-2-2-2-3-3-3-2-2-3-3-3-3111-2111-2-2111111000000000000000000000000000000000000
χ616666666-6-666-6-6-6-6-2-3-2-2-2-3-3-3-2-23333111211122-1-1-1-1-1-1000000000000000000000000000000000000
χ62666666-600-6-6000026-2226-6-6-2-200002220-2-2-200000000000000000000000000000000000000000000
χ63666666-600-6-600002-3-222-333-2-23333−33−33-1-1-1011100−3−3−3333000000000000000000000000000000000000
χ64666666-600-6-600002-3-222-333-2-2−33−333333-1-1-1011100333−3−3−3000000000000000000000000000000000000
χ6566−3−3i3−3+3i3−3−3i3−3+3i3666−3−3i3−3+3i3−3−3i3−3−3i3−3+3i3−3+3i3-20-21+i31−i30001+i31−i30000-21+i31−i3-2-21+i31−i31+i31−i3-21+i31−i3-21+i31−i3000000000000000000000000000000000000
χ6666−3−3i3−3+3i3−3−3i3−3+3i36-6-6−3−3i3−3+3i33+3i33+3i33−3i33−3i3-20-21+i31−i30001+i31−i30000-21+i31−i32-21+i31−i3−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000000000000000
χ6766−3−3i3−3+3i3−3−3i3−3+3i3-6003+3i33−3i3000020-2−1−i3−1+i30001+i31−i300002−1−i3−1+i30-21+i31−i300234ζ14+2ζ22−2ζ14−4ζ22−23−4ζ14−2ζ222ζ14+4ζ22000000000000000000000000000000000000
χ6866−3−3i3−3+3i3−3−3i3−3+3i3-6003+3i33−3i3000020-2−1−i3−1+i30001+i31−i300002−1−i3−1+i30-21+i31−i300−23−4ζ14−2ζ222ζ14+4ζ22234ζ14+2ζ22−2ζ14−4ζ22000000000000000000000000000000000000
χ6966−3−3i3−3+3i3−3−3i3−3+3i3-6003+3i33−3i3000020-2−1−i3−1+i30001+i31−i30000-42+2i32−2i304−2−2i3−2+2i300000000000000000000000000000000000000000000
χ7066−3−3i3−3+3i3−3−3i3−3+3i3-6003+3i33−3i30000-6063+3i33−3i3000−3−3i3−3+3i30000000000000000000000000000000000000000000000000000000
χ7166−3+3i3−3−3i3−3+3i3−3−3i3666−3+3i3−3−3i3−3+3i3−3+3i3−3−3i3−3−3i3-20-21−i31+i30001−i31+i30000-21−i31+i3-2-21−i31+i31−i31+i3-21−i31+i3-21−i31+i3000000000000000000000000000000000000
χ7266−3+3i3−3−3i3−3+3i3−3−3i36-6-6−3+3i3−3−3i33−3i33−3i33+3i33+3i3-20-21−i31+i30001−i31+i30000-21−i31+i32-21−i31+i3−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000000000000000
χ7366−3+3i3−3−3i3−3+3i3−3−3i3-6003−3i33+3i3000020-2−1+i3−1−i30001−i31+i300002−1+i3−1−i30-21−i31+i30023−2ζ14−4ζ224ζ14+2ζ22−232ζ14+4ζ22−4ζ14−2ζ22000000000000000000000000000000000000
χ7466−3+3i3−3−3i3−3+3i3−3−3i3-6003−3i33+3i3000020-2−1+i3−1−i30001−i31+i300002−1+i3−1−i30-21−i31+i300−232ζ14+4ζ22−4ζ14−2ζ2223−2ζ14−4ζ224ζ14+2ζ22000000000000000000000000000000000000
χ7566−3+3i3−3−3i3−3+3i3−3−3i3-6003−3i33+3i3000020-2−1+i3−1−i30001−i31+i30000-42−2i32+2i304−2+2i3−2−2i300000000000000000000000000000000000000000000
χ7666−3+3i3−3−3i3−3+3i3−3−3i3-6003−3i33+3i30000-6063−3i33+3i3000−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000
χ7712-12−6−6i3−6+6i36+6i36−6i30−6i26i2006ζ7+6ζ13−6ζ7−6ζ136ζ5+6ζ23−6ζ5−6ζ2300000000000000000000000000000000000000000000000000000000000000000
χ7812-12−6−6i3−6+6i36+6i36−6i306i2−6i200−6ζ7−6ζ136ζ7+6ζ13−6ζ5−6ζ236ζ5+6ζ2300000000000000000000000000000000000000000000000000000000000000000
χ7912-12−6+6i3−6−6i36−6i36+6i30−6i26i2006ζ5+6ζ23−6ζ5−6ζ236ζ7+6ζ13−6ζ7−6ζ1300000000000000000000000000000000000000000000000000000000000000000
χ8012-12−6+6i3−6−6i36−6i36+6i306i2−6i200−6ζ5−6ζ236ζ5+6ζ23−6ζ7−6ζ136ζ7+6ζ1300000000000000000000000000000000000000000000000000000000000000000

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