Finite Group Databasebeta

← Group #11771809

Character table — Group #11771809

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666666622344666666666666646666661212121212121212121212121212121244444444121212121212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-11-1-111-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1ii−i−i-1-1-1-11111iiii−i−i−i−iii−i−i
χ6111111111111111111-1-11-1-111-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii
χ7111111111111111111-1-11-1-111-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii
χ8111111111111111111-1-11-1-111-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−i
χ9222222222222222222222-2-22222222222222-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222222-2-222222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ112222222-122-122-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-122-122-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-122-122-1-122222-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-1-1-1-1-2-211-2-211111111110000000000000000−i3−i3i3i3−i3−i3i3i30000
χ142222222-122-122-1-122222-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-1-1-1-1-2-211-2-211111111110000000000000000i3i3−i3−i3i3i3−i3−i30000
χ152222222-122-122-1-1222-2-2-122-1-111-1-1-1-1-1-1-111-2-2-21111-2-21122-1-11111-1-1-1-1000000000000000033−3−3−3−3330000
χ162222222-122-122-1-1222-2-2-122-1-111-1-1-1-1-1-1-111-2-2-21111-2-21122-1-11111-1-1-1-10000000000000000−3−33333−3−30000
χ172222222-122-122-1-1222-2-2-1-2-2-1-111-1-1-1-1-1-1-1112-2-2111122-1-1-2-211-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii0000
χ182222222-122-122-1-1222-2-2-1-2-2-1-111-1-1-1-1-1-1-1112-2-2111122-1-1-2-211-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i0000
χ19222222-12-1-12-1-122-1-1-122-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-1-12-1-122-1-1-122-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-1-12-1-122-1-1-122-1-2-22222-1-1-1-1-1-1-122-2-1-1-1-1-1-111-2-211-2-21111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-1-12-1-122-1-1-122-1-2-22222-1-1-1-1-1-1-122-2-1-1-1-1-1-111-2-211-2-21111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-1-12-1-122-1-1-1-2-2-12222-2-2-1-1-1-1-1-1-1-2-2-211111111-2-2-1-1221111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ24222222-12-1-12-1-122-1-1-1-2-2-12222-2-2-1-1-1-1-1-1-1-2-2-211111111-2-2-1-1221111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ25222222-12-1-12-1-122-1-1-1-2-2-1-2-222-2-2-1-1-1-1-1-1-1-2-22111111-1-12211-2-2-1-1-1-1111122-2-200001111-1-1-1-1000000000000
χ26222222-12-1-12-1-122-1-1-1-2-2-1-2-222-2-2-1-1-1-1-1-1-1-2-22111111-1-12211-2-2-1-1-1-11111-2-2220000-1-1-1-11111000000000000
χ272-2-222-222222-2-2-2-2-2-220022i−2i2-200222-2-2-2-200000000000002i−2i2i−2i00002i2i−2i−2i00001+i−1−i1−i−1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ282-2-222-222222-2-2-2-2-2-220022i−2i2-200222-2-2-2-200000000000002i−2i2i−2i00002i2i−2i−2i0000−1−i1+i−1+i1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ292-2-222-222222-2-2-2-2-2-22002−2i2i2-200222-2-2-2-20000000000000−2i2i−2i2i0000−2i−2i2i2i00001−i−1+i1+i−1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ302-2-222-222222-2-2-2-2-2-22002−2i2i2-200222-2-2-2-20000000000000−2i2i−2i2i0000−2i−2i2i2i0000−1+i1−i−1−i1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ312-2-222-22-122-1-2-211-2-2200-12i−2i-11−i3i3-1-1-11111−i3i3000−i3−i3i3i3003−32i−2i−ii33−3−3−i−iii00001+i−1−i1−i−1+i00000000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000
χ322-2-222-22-122-1-2-211-2-2200-12i−2i-11−i3i3-1-1-11111−i3i3000−i3−i3i3i3003−32i−2i−ii33−3−3−i−iii0000−1−i1+i−1+i1−i00000000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000
χ332-2-222-22-122-1-2-211-2-2200-12i−2i-11i3−i3-1-1-11111i3−i3000i3i3−i3−i300−332i−2i−ii−3−333−i−iii00001+i−1−i1−i−1+i00000000−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000
χ342-2-222-22-122-1-2-211-2-2200-12i−2i-11i3−i3-1-1-11111i3−i3000i3i3−i3−i300−332i−2i−ii−3−333−i−iii0000−1−i1+i−1+i1−i00000000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000
χ352-2-222-22-122-1-2-211-2-2200-1−2i2i-11−i3i3-1-1-11111−i3i3000−i3−i3i3i300−33−2i2ii−i−3−333ii−i−i00001−i−1+i1+i−1−i00000000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000
χ362-2-222-22-122-1-2-211-2-2200-1−2i2i-11−i3i3-1-1-11111−i3i3000−i3−i3i3i300−33−2i2ii−i−3−333ii−i−i0000−1+i1−i−1−i1+i00000000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000
χ372-2-222-22-122-1-2-211-2-2200-1−2i2i-11i3−i3-1-1-11111i3−i3000i3i3−i3−i3003−3−2i2ii−i33−3−3ii−i−i00001−i−1+i1+i−1−i00000000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ140000
χ382-2-222-22-122-1-2-211-2-2200-1−2i2i-11i3−i3-1-1-11111i3−i3000i3i3−i3−i3003−3−2i2ii−i33−3−3ii−i−i0000−1+i1−i−1−i1+i00000000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000
χ392-2-22-2222-2-22-2-2-2-22222-2200-22222-2-222-2-2-2-202-22-22-20000000000000000000000000000000000000000−i2i2−i2i2
χ402-2-22-2222-2-22-2-2-2-22222-2200-22222-2-222-2-2-2-202-22-22-20000000000000000000000000000000000000000i2−i2i2−i2
χ412-2-22-2222-2-22-2-2-2-2222-22200-22-2-22-2-222-2-2220-22-22-2200000000000000000000000000000000000000002−2−22
χ422-2-22-2222-2-22-2-2-2-2222-22200-22-2-22-2-222-2-2220-22-22-220000000000000000000000000000000000000000−222−2
χ43444444-2-2-2-2-2-2-2-2-2-2-2-244144-2-2-2-21111111-2-24-2-21111-2-2-2-2-2-2-2-2111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2441-4-4-2-2-2-21111111-2-2-4-2-2111122222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-2-4-4144-2-222111111122-422-1-1-1-12222-2-2-2-2-1-1-1-111110000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-2-4-41-4-4-2-222111111122422-1-1-1-1-2-2-2-222221111-1-1-1-10000000000000000000000000000
χ474444-4-444-4-444444-4-4400400-4-4004-4-4-4-44400000000000000000000000000000000000000000000000000000
χ484444-4-44-2-4-4-244-2-2-4-4400-20022−2i32i3-22222-2-22i3−2i3000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ494444-4-44-2-4-4-244-2-2-4-4400-200222i3−2i3-22222-2-2−2i32i30002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ504444-4-4-24224-2-24422-200-200-4-400-22222-2-2000000000−2i32i3000000−2i32i3−2i32i300000000000000000000000000000000
χ514444-4-4-24224-2-24422-200-200-4-400-22222-2-20000000002i3−2i30000002i3−2i32i3−2i300000000000000000000000000000000
χ524444-4-4-2-222-2-2-2-2-222-20010022−2i32i31-1-1-1-1112i3−2i3000i3−i3−i3i3−2i32i3000000i3−i3i3−i33-33-30000000000000000000000000000
χ534444-4-4-2-222-2-2-2-2-222-20010022−2i32i31-1-1-1-1112i3−2i3000i3−i3−i3i32i3−2i3000000−i3i3−i3i3-33-330000000000000000000000000000
χ544444-4-4-2-222-2-2-2-2-222-200100222i3−2i31-1-1-1-111−2i32i3000−i3i3i3−i3−2i32i3000000i3−i3i3−i3-33-330000000000000000000000000000
χ554444-4-4-2-222-2-2-2-2-222-200100222i3−2i31-1-1-1-111−2i32i3000−i3i3i3−i32i3−2i3000000−i3i3−i3i33-33-30000000000000000000000000000
χ5644-4-4004400-44-44-400-4004000000-400004-40000000000000000000000000002i−2i00002i−2i2i−2i0000000000000000
χ5744-4-4004400-44-44-400-4004000000-400004-4000000000000000000000000000−2i2i0000−2i2i−2i2i0000000000000000
χ5844-4-400-24−2i32i3-4-224-4−2i32i3200-20000002−2i32i3−2i32i3-220000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ220000000000000000
χ5944-4-400-24−2i32i3-4-224-4−2i32i3200-20000002−2i32i3−2i32i3-22000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ220000000000000000
χ6044-4-400-242i3−2i3-4-224-42i3−2i3200-200000022i3−2i32i3−2i3-220000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ140000000000000000
χ6144-4-400-242i3−2i3-4-224-42i3−2i3200-200000022i3−2i32i3−2i3-22000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ140000000000000000
χ624-44-4004400-4-44-4400-4004000000-40000-4400000000000000000000000002i−2i00000000002i−2i2i−2i000000000000
χ634-44-4004400-4-44-4400-4004000000-40000-440000000000000000000000000−2i2i0000000000−2i2i−2i2i000000000000
χ644-44-400-24−2i32i3-42-2-442i3−2i3200-20000002−2i32i32i3−2i32-200000000000000000000000002i−2i00000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ654-44-400-24−2i32i3-42-2-442i3−2i3200-20000002−2i32i32i3−2i32-20000000000000000000000000−2i2i0000000000−2ζ222ζ22−2ζ142ζ14000000000000
χ664-44-400-242i3−2i3-42-2-44−2i32i3200-200000022i3−2i3−2i32i32-200000000000000000000000002i−2i00000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ674-44-400-242i3−2i3-42-2-44−2i32i3200-200000022i3−2i3−2i32i32-20000000000000000000000000−2i2i0000000000−2ζ142ζ14−2ζ222ζ22000000000000
χ684-4-444-4-24-2-2422-4-422-200-24i−4i4-400-2-2-222220000000000000−2i2i4i−4i0000−2i−2i2i2i0000000000000000000000000000
χ694-4-444-4-24-2-2422-4-422-200-2−4i4i4-400-2-2-2222200000000000002i−2i−4i4i00002i2i−2i−2i0000000000000000000000000000
χ704-4-444-4-2-2-2-2-2222222-20014i−4i-22−2i32i3111-1-1-1-1−2i32i3000i3i3−i3−i30023−23−2i2i−2i2i−3−333ii−i−i0000000000000000000000000000
χ714-4-444-4-2-2-2-2-2222222-20014i−4i-222i3−2i3111-1-1-1-12i3−2i3000−i3−i3i3i300−2323−2i2i−2i2i33−3−3ii−i−i0000000000000000000000000000
χ724-4-444-4-2-2-2-2-2222222-2001−4i4i-22−2i32i3111-1-1-1-1−2i32i3000i3i3−i3−i300−23232i−2i2i−2i33−3−3−i−iii0000000000000000000000000000
χ734-4-444-4-2-2-2-2-2222222-2001−4i4i-222i3−2i3111-1-1-1-12i3−2i3000−i3−i3i3i30023−232i−2i2i−2i−3−333−i−iii0000000000000000000000000000
χ744-4-44-444-2-4-4-2-4-4224444-4-2002-2-2-2-222-2-2222204-4-22-2200000000000000000000000000000000000000000000
χ754-4-44-444-2-4-4-2-4-422444-44-2002-222-222-2-222-2-20-442-22-200000000000000000000000000000000000000000000
χ764-4-44-44-2422422-4-4-2-2-24-4-200-4444-222-2-222-4-40-22-22-2200000000000000000000000000000000000000000000
χ774-4-44-44-2422422-4-4-2-2-2-44-200-44-4-4-222-2-2224402-22-22-200000000000000000000000000000000000000000000
χ784-4-44-44-2-222-22222-2-2-24-41002-2-2-21-1-111-1-1220-221-11-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ794-4-44-44-2-222-22222-2-2-24-41002-2-2-21-1-111-1-1220-221-11-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ804-4-44-44-2-222-22222-2-2-2-441002-2221-1-111-1-1-2-202-2-11-11000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ814-4-44-44-2-222-22222-2-2-2-441002-2221-1-111-1-1-2-202-2-11-1100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ8288-8-8008-40048-8-4400-800-400000040000-4400000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4−4i34i34-44-44−4i34i34002000000-22i3−2i32i3−2i32-200000000000000000000000000000000000000000000000000000
χ8488-8-800-4-44i3−4i34-44-444i3−4i34002000000-2−2i32i3−2i32i32-200000000000000000000000000000000000000000000000000000
χ858-88-8008-4004-884-400-800-4000000400004-400000000000000000000000000000000000000000000000000000
χ868-88-800-4-4−4i34i344-44-44i3−4i34002000000-22i3−2i3−2i32i3-2200000000000000000000000000000000000000000000000000000
χ878-88-800-4-44i3−4i344-44-4−4i34i34002000000-2−2i32i32i3−2i3-2200000000000000000000000000000000000000000000000000000

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