Finite Group Databasebeta

← Group #13135157

Character table — Group #13135157

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122222344666121212124661212336666666666366666666612121212121212121212121212121212444488881212121212121212242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-11-1-1111-1-1-1-11-1-1111111-1-1111-1-111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1
χ61111-1-11-1-1111-1-1-1-11-1-1111111-1-1111-1-111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111
χ71111-1-11-1-1111-1-1-1-11-1-1111111-1-1111-1-111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111
χ81111-1-11-1-1111-1-1-1-11-1-1111111-1-1111-1-111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1
χ92222222222222222222222-12222-12-122-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-12222-12-122-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-1-1-12-12-1-12-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ12222222222222222222222-12-1-1-1-12-12-1-12-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ132222222-2-2222-2-2-2-2-222-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-222-2-22-12222-12-122-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000000000000000000000−i3i3−i3i3
χ152222222-2-2222-2-2-2-2-222-2-22-12222-12-122-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000000000000000000000i3−i3i3−i3
χ162222222-2-2222-2-2-2-2-222-2-2-12-1-1-1-12-12-1-12-122-1-1-1-1-1-1-111-2-211-2-21111111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ172222222-2-2222-2-2-2-2-222-2-2-12-1-1-1-12-12-1-12-122-1-1-1-1-1-1-111-2-211-2-21111111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ182222-2-22222222222-2-2-2-2-22222-2-2222-2-222-2-222-2-2-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000000000
χ192222-2-22222222222-2-2-2-2-22-122-2-2-12-1-2-2-1-111-1-11111-1-2-21122-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ202222-2-22222222222-2-2-2-2-22-122-2-2-12-1-2-2-1-111-1-11111-1-2-21122-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ212222-2-22222222222-2-2-2-2-2-12-1-1112-12112-1-2-2-1-11111-111-2-2-1-1221111-1-1-1-10000000033−3−3−3−33300000000000000
χ222222-2-22222222222-2-2-2-2-2-12-1-1112-12112-1-2-2-1-11111-111-2-2-1-1221111-1-1-1-100000000−3−33333−3−300000000000000
χ232222-2-22-2-2222-2-2-2-22-2-2222-122-2-2-12-1-2-2-1-111-1-11111-122-1-1-2-211-1-1-1-111110000000000000000000000002-2-1-111
χ242222-2-22-2-2222-2-2-2-22-2-2222-122-2-2-12-1-2-2-1-111-1-11111-122-1-1-2-211-1-1-1-11111000000000000000000000000-2211-1-1
χ252222-2-22-2-2222-2-2-2-22-2-222-12-1-1112-12112-1-2-2-1-11111-1-1-12211-2-2-1-1-1-111112i2i−2i−2i0000−i−i−i−iiiii00000000000000
χ262222-2-22-2-2222-2-2-2-22-2-222-12-1-1112-12112-1-2-2-1-11111-1-1-12211-2-2-1-1-1-11111−2i−2i2i2i0000iiii−i−i−i−i00000000000000
χ2722-2-20022i−2i2-2-22i2i−2i−2i00000222-2002-2-200-22002-20000-200002i−2i2i−2i00002i2i−2i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ2822-2-20022i−2i2-2-22i2i−2i−2i00000222-2002-2-200-22002-20000-200002i−2i2i−2i00002i2i−2i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ2922-2-20022i−2i2-2-22i2i−2i−2i00000-12-11−i3i321-2−i3i3-2-100-11−i3−i3i3i313−300−ii2i−2i33−3−3−i−iii1+i−1−i1−i−1+i0000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ2200000000000000
χ3022-2-20022i−2i2-2-22i2i−2i−2i00000-12-11−i3i321-2−i3i3-2-100-11−i3−i3i3i313−300−ii2i−2i33−3−3−i−iii−1−i1+i−1+i1−i0000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ2200000000000000
χ3122-2-20022i−2i2-2-22i2i−2i−2i00000-12-11i3−i321-2i3−i3-2-100-11i3i3−i3−i31−3300−ii2i−2i−3−333−i−iii1+i−1−i1−i−1+i0000−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ1400000000000000
χ3222-2-20022i−2i2-2-22i2i−2i−2i00000-12-11i3−i321-2i3−i3-2-100-11i3i3−i3−i31−3300−ii2i−2i−3−333−i−iii−1−i1+i−1+i1−i0000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ1400000000000000
χ3322-2-2002−2i2i2-2-2−2i−2i2i2i00000222-2002-2-200-22002-20000-20000−2i2i−2i2i0000−2i−2i2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ3422-2-2002−2i2i2-2-2−2i−2i2i2i00000222-2002-2-200-22002-20000-20000−2i2i−2i2i0000−2i−2i2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ3522-2-2002−2i2i2-2-2−2i−2i2i2i00000-12-11−i3i321-2−i3i3-2-100-11−i3−i3i3i31−3300i−i−2i2i−3−333ii−i−i1−i−1+i1+i−1−i0000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ2200000000000000
χ3622-2-2002−2i2i2-2-2−2i−2i2i2i00000-12-11−i3i321-2−i3i3-2-100-11−i3−i3i3i31−3300i−i−2i2i−3−333ii−i−i−1+i1−i−1−i1+i0000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ2200000000000000
χ3722-2-2002−2i2i2-2-2−2i−2i2i2i00000-12-11i3−i321-2i3−i3-2-100-11i3i3−i3−i313−300i−i−2i2i33−3−3ii−i−i1−i−1+i1+i−1−i0000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ1400000000000000
χ3822-2-2002−2i2i2-2-2−2i−2i2i2i00000-12-11i3−i321-2i3−i3-2-100-11i3i3−i3−i313−300i−i−2i2i33−3−3ii−i−i−1+i1−i−1−i1+i0000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ1400000000000000
χ392-2-222-2200-22-2000002-20022-2222-2-2-2-2-2222-2-222-22-2-200000000000000000000−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i2000000
χ402-2-222-2200-22-2000002-20022-2222-2-2-2-2-2222-2-222-22-2-200000000000000000000i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i2000000
χ412-2-22-22200-22-200000-220022-22-2-2-2-2-22222-22-22-22-22-2000000000000000000002−2−220000000022−2−2−2−222000000
χ422-2-22-22200-22-200000-220022-22-2-2-2-2-22222-22-22-22-22-200000000000000000000−222−200000000−2−22222−2−2000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ454444-4-44444444444-4-4-4-4-4-2-2-2-222-2-2-222-212211-1-1-1-112222-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ464444-4-44-4-4444-4-4-4-44-4-444-2-2-2-222-2-2-222-212211-1-1-1-11-2-2-2-222221111-1-1-1-1000000000000000000000000000000
χ4744-4-40044i−4i4-4-44i4i−4i−4i000004-24-400-2-42002-200-220000200004i−4i−2i2i0000−2i−2i2i2i000000000000000000000000000000
χ4844-4-40044i−4i4-4-44i4i−4i−4i00000-2-2-22−2i32i3-222−2i32i321001-1i3i3−i3−i3-123−2300−2i2i−2i2i−3−333ii−i−i000000000000000000000000000000
χ4944-4-40044i−4i4-4-44i4i−4i−4i00000-2-2-222i3−2i3-2222i3−2i321001-1−i3−i3i3i3-1−232300−2i2i−2i2i33−3−3ii−i−i000000000000000000000000000000
χ5044-4-4004−4i4i4-4-4−4i−4i4i4i000004-24-400-2-42002-200-22000020000−4i4i2i−2i00002i2i−2i−2i000000000000000000000000000000
χ5144-4-4004−4i4i4-4-4−4i−4i4i4i00000-2-2-22−2i32i3-222−2i32i321001-1i3i3−i3−i3-1−2323002i−2i2i−2i33−3−3−i−iii000000000000000000000000000000
χ5244-4-4004−4i4i4-4-4−4i−4i4i4i00000-2-2-222i3−2i3-2222i3−2i321001-1−i3−i3i3i3-123−23002i−2i2i−2i−3−333−i−iii000000000000000000000000000000
χ534-44-400400-4-4400000000044-4-400-44400-4400-4-4000040000000000000000000000000000000000000000000000
χ544-44-400400-4-440000000004-2-4-40024-2002-200220000-200−2i32i30000−2i32i3−2i32i30000000000000000000000000000000000
χ554-44-400400-4-440000000004-2-4-40024-2002-200220000-2002i3−2i300002i3−2i32i3−2i30000000000000000000000000000000000
χ564-44-400400-4-44000000000-2422−2i32i3-4-242i3−2i3-4-20022−2i32i32i3−2i3-20000000000000000000000000000000000000000000000
χ574-44-400400-4-44000000000-24222i3−2i3-4-24−2i32i3-4-200222i3−2i3−2i32i3-20000000000000000000000000000000000000000000000
χ584-44-400400-4-44000000000-2-222−2i32i32-2-22i3−2i32100-1-1i3−i3−i3i3100−2i32i30000i3−i3i3−i33-33-3000000000000000000000000000000
χ594-44-400400-4-44000000000-2-222−2i32i32-2-22i3−2i32100-1-1i3−i3−i3i31002i3−2i30000−i3i3−i3i3-33-33000000000000000000000000000000
χ604-44-400400-4-44000000000-2-2222i3−2i32-2-2−2i32i32100-1-1−i3i3i3−i3100−2i32i30000i3−i3i3−i3-33-33000000000000000000000000000000
χ614-44-400400-4-44000000000-2-2222i3−2i32-2-2−2i32i32100-1-1−i3i3i3−i31002i3−2i30000−i3i3−i3i33-33-3000000000000000000000000000000
χ624-4-444-4400-44-4000004-4004-2-44442-42-4-4-2-2-222-2-22-2220000000000000000000000000000000000000000000000
χ634-4-444-4400-44-4000004-400-242-2-2-2-42-4224-24-42-2-22-2220000000000000000000000000000000000000000000000
χ644-4-444-4400-44-4000004-400-2-22-2-2-222222-21-22-111-11-1-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000
χ654-4-444-4400-44-4000004-400-2-22-2-2-222222-21-22-111-11-1-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000
χ664-4-44-44400-44-400000-44004-2-44-4-42-4244-2-22-22-22-22-220000000000000000000000000000000000000000000000
χ674-4-44-44400-44-400000-4400-242-222-42-4-2-24-2-442-22-22-220000000000000000000000000000000000000000000000
χ684-4-44-44400-44-400000-4400-2-22-222222-2-2-212-2-11-11-11-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000
χ694-4-44-44400-44-400000-4400-2-22-222222-2-2-212-2-11-11-11-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000
χ70666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-1000000
χ71666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-20000000011111111000000
χ72666666-3-6-6-3-3-33333-6-3-3330000000000000000000000000000000000000000000000000000003−33−33−33−3000000
χ73666666-3-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000000000000000−33−33−33−33000000
χ746666-6-6-366-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ756666-6-6-366-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ766666-6-6-3-6-6-3-3-33333633-3-30000000000000000000000000000000000000000002i2i−2i−2i00000000−i−i−i−iiiii000000
χ776666-6-6-3-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000−2i−2i2i2i00000000iiii−i−i−i−i000000
χ786-6-666-6-3003-3333−3333−330-3333−33000000000000000000000000000000000000000000−i2i2−i2i200000000ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ796-6-666-6-3003-3333−3333−330-3333−33000000000000000000000000000000000000000000i2−i2i2−i200000000−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ806-6-666-6-3003-33−3333−33330-33−3333000000000000000000000000000000000000000000−i2i2−i2i200000000ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ816-6-666-6-3003-33−3333−33330-33−3333000000000000000000000000000000000000000000i2−i2i2−i200000000−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ826-6-66-66-3003-3333−3333−3303-3−33330000000000000000000000000000000000000000002−2−2200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ836-6-66-66-3003-3333−3333−3303-3−3333000000000000000000000000000000000000000000−222−200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ846-6-66-66-3003-33−3333−333303-333−330000000000000000000000000000000000000000002−2−2200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ856-6-66-66-3003-33−3333−333303-333−33000000000000000000000000000000000000000000−222−200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ861212-12-1200-612i−12i-666−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-1200-6−12i12i-6666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-1212-1200-60066-6−6i36i36i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-1212-1200-60066-66i3−6i3−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000

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