Finite Group Databasebeta

← Group #13135167

Character table — Group #13135167

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122222344666466121212123366666666661212121236666666661212121212121212121212121212444488881212121212121212242424242424242424661212
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
χ51111-1-11-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1
χ61111-1-11-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111
χ71111-1-11-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111
χ81111-1-11-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1
χ922222222222222222222-122-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ1022222222222222222222-122-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ112222222222222222222-12-1-122-1-1-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ122222222222222222222-12-1-122-1-1-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ132222222-2-2222-222-2-2-2-2222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-222-2-2-2-22-122-1-1222-1221111-1-1-1-1-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−3000000
χ152222222-2-2222-222-2-2-2-22-122-1-1222-1221111-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−333000000
χ162222222-2-2222-222-2-2-2-2-12-1-122-1-1-12-1-1-2-2-2-2-122-1-1-1-1-1-1-111-2-2111111111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ172222222-2-2222-222-2-2-2-2-12-1-122-1-1-12-1-1-2-2-2-2-122-1-1-1-1-1-1-111-2-2111111111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ182222-2-2222222-2-2-2-2-222222222-2-222-2-222222-2-222-2-2-2-22-2-2-2-222-2-2-2-22222000000000000000000000000000000
χ192222-2-2222222-2-2-2-2-2222-122-1-1-2-22-1-2-2-1-1-1-1-111-1-11111-1-2-211221111-1-1-1-10000000000000000−i3−i3i3i3i3i3−i3−i3000000
χ202222-2-2222222-2-2-2-2-2222-122-1-1-2-22-1-2-2-1-1-1-1-111-1-11111-1-2-211221111-1-1-1-10000000000000000i3i3−i3−i3−i3−i3i3i3000000
χ212222-2-2222222-2-2-2-2-222-12-1-12211-12112222-1-2-2-1-11111-111-2-2-1-11111-1-1-1-10000000033−3−3−3−33300000000000000
χ222222-2-2222222-2-2-2-2-222-12-1-12211-12112222-1-2-2-1-11111-111-2-2-1-11111-1-1-1-100000000−3−33333−3−300000000000000
χ232222-2-22-2-22222-2-222-2-22-122-1-1-2-22-1-2-21111-111-1-11111-122-1-1-2-2-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii000000
χ242222-2-22-2-22222-2-222-2-22-122-1-1-2-22-1-2-21111-111-1-11111-122-1-1-2-2-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i000000
χ252222-2-22-2-22222-2-222-2-2-12-1-12211-1211-2-2-2-2-1-2-2-1-11111-1-1-12211-1-1-1-111112i2i−2i−2i0000−i−i−i−iiiii00000000000000
χ262222-2-22-2-22222-2-222-2-2-12-1-12211-1211-2-2-2-2-1-2-2-1-11111-1-1-12211-1-1-1-11111−2i−2i2i2i0000iiii−i−i−i−i00000000000000
χ2722-2-20022i−2i2-2-2000002i−2i222-22-200-2-2002i2i−2i−2i2002-20000-200002i−2i00002i2i−2i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ2822-2-20022i−2i2-2-2000002i−2i222-22-200-2-2002i2i−2i−2i2002-20000-200002i−2i00002i2i−2i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ2922-2-20022i−2i2-2-2000002i−2i-12-112-2−i3i31-2−i3i32i2i−2i−2i-100-11−i3−i3i3i313−300−ii33−3−3−i−iii1+i−1−i1−i−1+i0000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ2200000000000000
χ3022-2-20022i−2i2-2-2000002i−2i-12-112-2−i3i31-2−i3i32i2i−2i−2i-100-11−i3−i3i3i313−300−ii33−3−3−i−iii−1−i1+i−1+i1−i0000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ2200000000000000
χ3122-2-20022i−2i2-2-2000002i−2i-12-112-2i3−i31-2i3−i32i2i−2i−2i-100-11i3i3−i3−i31−3300−ii−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−2i2-2-2000002i−2i-12-112-2i3−i31-2i3−i32i2i−2i−2i-100-11i3i3−i3−i31−3300−ii−3−333−i−iii−1−i1+i−1+i1−i0000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ1400000000000000
χ3322-2-2002−2i2i2-2-200000−2i2i222-22-200-2-200−2i−2i2i2i2002-20000-20000−2i2i0000−2i−2i2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ3422-2-2002−2i2i2-2-200000−2i2i222-22-200-2-200−2i−2i2i2i2002-20000-20000−2i2i0000−2i−2i2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ3522-2-2002−2i2i2-2-200000−2i2i-12-112-2−i3i31-2−i3i3−2i−2i2i2i-100-11−i3−i3i3i31−3300i−i−3−333ii−i−i1−i−1+i1+i−1−i0000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ2200000000000000
χ3622-2-2002−2i2i2-2-200000−2i2i-12-112-2−i3i31-2−i3i3−2i−2i2i2i-100-11−i3−i3i3i31−3300i−i−3−333ii−i−i−1+i1−i−1−i1+i0000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ2200000000000000
χ3722-2-2002−2i2i2-2-200000−2i2i-12-112-2i3−i31-2i3−i3−2i−2i2i2i-100-11i3i3−i3−i313−300i−i33−3−3ii−i−i1−i−1+i1+i−1−i0000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ1400000000000000
χ3822-2-2002−2i2i2-2-200000−2i2i-12-112-2i3−i31-2i3−i3−2i−2i2i2i-100-11i3i3−i3−i313−300i−i33−3−3ii−i−i−1+i1−i−1−i1+i0000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ1400000000000000
χ392-2-222-2200-2-2202-2000022-22-2222-2-2-2-2000022-2-222-22-2-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2000000
χ402-2-222-2200-2-2202-2000022-22-2222-2-2-2-2000022-2-222-22-2-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2000000
χ412-2-222-2200-2-2202-200002-1-221-122-21-2-23−33−3-1-111-1-11-111003−3003−33−33−33−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ422-2-222-2200-2-2202-200002-1-221-122-21-2-23−33−3-1-111-1-11-111003−3003−33−33−33−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ432-2-222-2200-2-2202-200002-1-221-122-21-2-2−33−33-1-111-1-11-11100−3300−33−33−33−330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ442-2-222-2200-2-2202-200002-1-221-122-21-2-2−33−33-1-111-1-11-11100−3300−33−33−33−330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ452-2-22-22200-2-220-22000022-22-22-2-2-2-22200002-22-22-22-22-20000000000000000002−2−22000000002−22−2−22−22000000
χ462-2-22-22200-2-220-22000022-22-22-2-2-2-22200002-22-22-22-22-2000000000000000000−222−200000000−22−222−22−2000000
χ472-2-22-22200-2-220-2200002-1-221-1-2-2-21223−33−3-11-11-11-11-1100−3300−33−333−33−300002−2−2200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ482-2-22-22200-2-220-2200002-1-221-1-2-2-21223−33−3-11-11-11-11-1100−3300−33−333−33−30000−222−200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ492-2-22-22200-2-220-2200002-1-221-1-2-2-2122−33−33-11-11-11-11-11003−3003−33−3−33−3300002−2−2200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ502-2-22-22200-2-220-2200002-1-221-1-2-2-2122−33−33-11-11-11-11-11003−3003−33−3−33−330000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ514444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ524444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ534444-4-4444444-4-4-4-4-444-2-2-2-2-2-222-2-222-2-2-2-212211-1-1-1-112222-2-2-1-1-1-11111000000000000000000000000000000
χ544444-4-44-4-44444-4-444-4-4-2-2-2-2-2-222-2-222222212211-1-1-1-11-2-2-2-2221111-1-1-1-1000000000000000000000000000000
χ5544-4-40044i−4i4-4-4000004i−4i4-24-4-2200-4200−2i−2i2i2i-200-220000200004i−4i0000−2i−2i2i2i000000000000000000000000000000
χ5644-4-40044i−4i4-4-4000004i−4i-2-2-22-22−2i32i322−2i32i3−2i−2i2i2i1001-1i3i3−i3−i3-123−2300−2i2i−3−333ii−i−i000000000000000000000000000000
χ5744-4-40044i−4i4-4-4000004i−4i-2-2-22-222i3−2i3222i3−2i3−2i−2i2i2i1001-1−i3−i3i3i3-1−232300−2i2i33−3−3ii−i−i000000000000000000000000000000
χ5844-4-4004−4i4i4-4-400000−4i4i4-24-4-2200-42002i2i−2i−2i-200-22000020000−4i4i00002i2i−2i−2i000000000000000000000000000000
χ5944-4-4004−4i4i4-4-400000−4i4i-2-2-22-22−2i32i322−2i32i32i2i−2i−2i1001-1i3i3−i3−i3-1−2323002i−2i33−3−3−i−iii000000000000000000000000000000
χ6044-4-4004−4i4i4-4-400000−4i4i-2-2-22-222i3−2i3222i3−2i32i2i−2i−2i1001-1−i3−i3i3i3-123−23002i−2i−3−333−i−iii000000000000000000000000000000
χ614-44-400400-44-4000000044-4-4-4-40044000000400-4-40000400000000000000000000000000000000000000000000
χ624-44-400400-44-400000004-2-4-422004-200−2i32i32i3−2i3-200220000-20000000000−2i32i32i3−2i3000000000000000000000000000000
χ634-44-400400-44-400000004-2-4-422004-2002i3−2i3−2i32i3-200220000-200000000002i3−2i3−2i32i3000000000000000000000000000000
χ644-44-400400-44-40000000-2422-4-4−2i32i3-242i3−2i30000-20022−2i32i32i3−2i3-200000000000000000000000000000000000000000000
χ654-44-400400-44-40000000-2422-4-42i3−2i3-24−2i32i30000-200222i3−2i3−2i32i3-200000000000000000000000000000000000000000000
χ664-44-400400-44-40000000-2-22222−2i32i3-2-22i3−2i3−2i32i32i3−2i3100-1-1i3−i3−i3i31000000-333-3i3−i3−i3i3000000000000000000000000000000
χ674-44-400400-44-40000000-2-22222−2i32i3-2-22i3−2i32i3−2i3−2i32i3100-1-1i3−i3−i3i310000003-3-33−i3i3i3−i3000000000000000000000000000000
χ684-44-400400-44-40000000-2-222222i3−2i3-2-2−2i32i3−2i32i32i3−2i3100-1-1−i3i3i3−i310000003-3-33i3−i3−i3i3000000000000000000000000000000
χ694-44-400400-44-40000000-2-222222i3−2i3-2-2−2i32i32i3−2i3−2i32i3100-1-1−i3i3i3−i31000000-333-3−i3i3i3−i3000000000000000000000000000000
χ704-4-444-4400-4-4404-40000-242-2-44-2-22-4220000-24-42-2-22-22200000000000000000000000000000000000000000000
χ714-4-444-4400-4-4404-40000-2-22-22-2-2-2222223−2323−231-22-111-11-1-10023−2300−33−33−33−33000000000000000000000000000000
χ724-4-444-4400-4-4404-40000-2-22-22-2-2-22222−2323−23231-22-111-11-1-100−2323003−33−33−33−3000000000000000000000000000000
χ734-4-44-44400-4-440-440000-242-2-44222-4-2-20000-2-442-22-22-2200000000000000000000000000000000000000000000
χ744-4-44-44400-4-440-440000-2-22-22-22222-2-223−2323−2312-2-11-11-11-100−2323003−33−3−33−33000000000000000000000000000000
χ754-4-44-44400-4-440-440000-2-22-22-22222-2-2−2323−232312-2-11-11-11-10023−2300−33−333−33−3000000000000000000000000000000
χ76666666-366-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000000000000000022-1-1-1-1
χ77666666-366-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000000000000000000-2-21111
χ78666666-3-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3
χ79666666-3-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3
χ806666-6-6-366-3-3-3-63333-3-3000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3
χ816666-6-6-366-3-3-3-63333-3-3000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3
χ826666-6-6-3-6-6-3-3-3633-3-33300000000000000000000000000000000000000000000000000000000000000002-2-1-111
χ836666-6-6-3-6-6-3-3-3633-3-3330000000000000000000000000000000000000000000000000000000000000000-2211-1-1
χ841212-12-1200-612i−12i-66600000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-1200-6−12i12i-666000006i−6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-1200-6006-66000−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-1200-6006-660006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121212-12-60066-60-6600000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-1212-60066-606-600000000000000000000000000000000000000000000000000000000000000000000000000

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