Finite Group Databasebeta

← Group #11771945

Character table — Group #11771945

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
χ112222222-1222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-1222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-1222-12-1-122222-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-1-1-1-1-2-21111-2-2111111110000000000000000−i3−i3i3i3−i3−i3i3i30000
χ142222222-1222-12-1-122222-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-1-1-1-1-2-21111-2-2111111110000000000000000i3i3−i3−i3i3i3−i3−i30000
χ152222222-1222-12-1-1222-2-2-122-1-111-1-1-1-1-1-1-111-2-2-21111-2-211-1-1221111-1-1-1-1000000000000000033−3−3−3−3330000
χ162222222-1222-12-1-1222-2-2-122-1-111-1-1-1-1-1-1-111-2-2-21111-2-211-1-1221111-1-1-1-10000000000000000−3−33333−3−30000
χ172222222-1222-12-1-1222-2-2-1-2-2-1-111-1-1-1-1-1-1-1112-2-2111122-1-111-2-2-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii0000
χ182222222-1222-12-1-1222-2-2-1-2-2-1-111-1-1-1-1-1-1-1112-2-2111122-1-111-2-2-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i0000
χ19222222-12-1-1-12-122-1-1-122-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-1-1-12-122-1-1-122-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-1-1-12-122-1-1-122-1-2-22222-1-1-1-1-1-1-122-2-1-1-1-1-1-111-2-2-2-2111111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-1-1-12-122-1-1-122-1-2-22222-1-1-1-1-1-1-122-2-1-1-1-1-1-111-2-2-2-2111111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-1-1-12-122-1-1-1-2-2-12222-2-2-1-1-1-1-1-1-1-2-2-211111111-2-222-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ24222222-12-1-1-12-122-1-1-1-2-2-12222-2-2-1-1-1-1-1-1-1-2-2-211111111-2-222-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ25222222-12-1-1-12-122-1-1-1-2-2-1-2-222-2-2-1-1-1-1-1-1-1-2-22111111-1-122-2-211-1-1-1-1111122-2-200001111-1-1-1-1000000000000
χ26222222-12-1-1-12-122-1-1-1-2-2-1-2-222-2-2-1-1-1-1-1-1-1-2-22111111-1-122-2-211-1-1-1-11111-2-2220000-1-1-1-11111000000000000
χ2722-2-22-2222222-2-2-2-2-2-22-22002-222222-2-2-2-2-2-202-222-2-200000000000000000000000000000000000000002−22−2
χ2822-2-22-2222222-2-2-2-2-2-22-22002-222222-2-2-2-2-2-202-222-2-20000000000000000000000000000000000000000−22−22
χ2922-2-22-2222222-2-2-2-2-2-2-222002-2-2-2222-2-2-2-2220-22-2-2220000000000000000000000000000000000000000−i2i2i2−i2
χ3022-2-22-2222222-2-2-2-2-2-2-222002-2-2-2222-2-2-2-2220-22-2-2220000000000000000000000000000000000000000i2−i2−i2i2
χ3122-2-2-22222-2-22-2-2-222-20022i−2i-22002-2-222-2-200000000000002i−2i2i−2i00002i2i−2i−2i00001+i−1−i1−i−1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ3222-2-2-22222-2-22-2-2-222-20022i−2i-22002-2-222-2-200000000000002i−2i2i−2i00002i2i−2i−2i0000−1−i1+i−1+i1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ3322-2-2-22222-2-22-2-2-222-2002−2i2i-22002-2-222-2-20000000000000−2i2i−2i2i0000−2i−2i2i2i00001−i−1+i1+i−1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ3422-2-2-22222-2-22-2-2-222-2002−2i2i-22002-2-222-2-20000000000000−2i2i−2i2i0000−2i−2i2i2i0000−1+i1−i−1−i1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ3522-2-2-222-12-2-2-1-21122-200-12i−2i1-1−i3i3-111-1-111−i3i3000−i3i3−i3i3003−3−ii2i−2i33−3−3−i−iii00001+i−1−i1−i−1+i00000000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000
χ3622-2-2-222-12-2-2-1-21122-200-12i−2i1-1−i3i3-111-1-111−i3i3000−i3i3−i3i3003−3−ii2i−2i33−3−3−i−iii0000−1−i1+i−1+i1−i00000000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000
χ3722-2-2-222-12-2-2-1-21122-200-12i−2i1-1i3−i3-111-1-111i3−i3000i3−i3i3−i300−33−ii2i−2i−3−333−i−iii00001+i−1−i1−i−1+i00000000−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000
χ3822-2-2-222-12-2-2-1-21122-200-12i−2i1-1i3−i3-111-1-111i3−i3000i3−i3i3−i300−33−ii2i−2i−3−333−i−iii0000−1−i1+i−1+i1−i00000000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000
χ3922-2-2-222-12-2-2-1-21122-200-1−2i2i1-1−i3i3-111-1-111−i3i3000−i3i3−i3i300−33i−i−2i2i−3−333ii−i−i00001−i−1+i1+i−1−i00000000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000
χ4022-2-2-222-12-2-2-1-21122-200-1−2i2i1-1−i3i3-111-1-111−i3i3000−i3i3−i3i300−33i−i−2i2i−3−333ii−i−i0000−1+i1−i−1−i1+i00000000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000
χ4122-2-2-222-12-2-2-1-21122-200-1−2i2i1-1i3−i3-111-1-111i3−i3000i3−i3i3−i3003−3i−i−2i2i33−3−3ii−i−i00001−i−1+i1+i−1−i00000000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ140000
χ4222-2-2-222-12-2-2-1-21122-200-1−2i2i1-1i3−i3-111-1-111i3−i3000i3−i3i3−i3003−3i−i−2i2i33−3−3ii−i−i0000−1+i1−i−1−i1+i00000000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000
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
χ474444-4-4444-4-44444-4-4400400-4-4004-4-4-4-44400000000000000000000000000000000000000000000000000000
χ484444-4-44-24-4-4-24-2-2-4-4400-20022−2i32i3-22222-2-22i3−2i3000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ494444-4-44-24-4-4-24-2-2-4-4400-200222i3−2i3-22222-2-2−2i32i30002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ504444-4-4-24-2224-24422-200-200-4-400-22222-2-2000000000−2i32i3000000−2i32i3−2i32i300000000000000000000000000000000
χ514444-4-4-24-2224-24422-200-200-4-400-22222-2-20000000002i3−2i30000002i3−2i32i3−2i300000000000000000000000000000000
χ524444-4-4-2-2-222-2-2-2-222-20010022−2i32i31-1-1-1-1112i3−2i3000i3−i3−i3i3−2i32i3000000i3−i3i3−i33-33-30000000000000000000000000000
χ534444-4-4-2-2-222-2-2-2-222-20010022−2i32i31-1-1-1-1112i3−2i3000i3−i3−i3i32i3−2i3000000−i3i3−i3i3-33-330000000000000000000000000000
χ544444-4-4-2-2-222-2-2-2-222-200100222i3−2i31-1-1-1-111−2i32i3000−i3i3i3−i3−2i32i3000000i3−i3i3−i3-33-330000000000000000000000000000
χ554444-4-4-2-2-222-2-2-2-222-200100222i3−2i31-1-1-1-111−2i32i3000−i3i3i3−i32i3−2i3000000−i3i3−i3i33-33-30000000000000000000000000000
χ5644-4-44-44-2444-2-422-4-4-44-4-200-22-2-2-2-2-222222204-4-2-22200000000000000000000000000000000000000000000
χ5744-4-44-44-2444-2-422-4-4-4-44-200-2222-2-2-22222-2-20-4422-2-200000000000000000000000000000000000000000000
χ5844-4-44-4-24-2-2-242-4-42224-4-2004-444-2-2-22222-4-40-22-2-22200000000000000000000000000000000000000000000
χ5944-4-44-4-24-2-2-242-4-4222-44-2004-4-4-4-2-2-222224402-222-2-200000000000000000000000000000000000000000000
χ6044-4-44-4-2-2-2-2-2-22222224-4100-22-2-2111-1-1-1-1220-2211-1-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ6144-4-44-4-2-2-2-2-2-22222224-4100-22-2-2111-1-1-1-1220-2211-1-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ6244-4-44-4-2-2-2-2-2-2222222-44100-2222111-1-1-1-1-2-202-2-1-111000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ6344-4-44-4-2-2-2-2-2-2222222-44100-2222111-1-1-1-1-2-202-2-1-11100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ6444-4-4-44-24-22242-4-4-2-2200-24i−4i-4400-222-2-22200000000000004i−4i−2i2i0000−2i−2i2i2i0000000000000000000000000000
χ6544-4-4-44-24-22242-4-4-2-2200-2−4i4i-4400-222-2-2220000000000000−4i4i2i−2i00002i2i−2i−2i0000000000000000000000000000
χ6644-4-4-44-2-2-222-2222-2-220014i−4i2-2−2i32i31-1-111-1-1−2i32i3000i3−i3i3−i30023−23−2i2i−2i2i−3−333ii−i−i0000000000000000000000000000
χ6744-4-4-44-2-2-222-2222-2-220014i−4i2-22i3−2i31-1-111-1-12i3−2i3000−i3i3−i3i300−2323−2i2i−2i2i33−3−3ii−i−i0000000000000000000000000000
χ6844-4-4-44-2-2-222-2222-2-22001−4i4i2-2−2i32i31-1-111-1-1−2i32i3000i3−i3i3−i300−23232i−2i2i−2i33−3−3−i−iii0000000000000000000000000000
χ6944-4-4-44-2-2-222-2222-2-22001−4i4i2-22i3−2i31-1-111-1-12i3−2i3000−i3i3−i3i30023−232i−2i2i−2i−3−333−i−iii0000000000000000000000000000
χ704-44-40044-400-444-400-4004000000-400004-400000000000000000000000002i−2i00000000002i−2i2i−2i000000000000
χ714-44-40044-400-444-400-4004000000-400004-40000000000000000000000000−2i2i0000000000−2i2i−2i2i000000000000
χ724-44-400-242−2i32i3-4-24-4−2i32i3200-20000002−2i32i3−2i32i3-2200000000000000000000000002i−2i00000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ734-44-400-242−2i32i3-4-24-4−2i32i3200-20000002−2i32i3−2i32i3-220000000000000000000000000−2i2i0000000000−2ζ222ζ22−2ζ142ζ14000000000000
χ744-44-400-2422i3−2i3-4-24-42i3−2i3200-200000022i3−2i32i3−2i3-2200000000000000000000000002i−2i00000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ754-44-400-2422i3−2i3-4-24-42i3−2i3200-200000022i3−2i32i3−2i3-220000000000000000000000000−2i2i0000000000−2ζ142ζ14−2ζ222ζ22000000000000
χ764-4-440044-400-4-4-44004004000000-40000-440000000000000000000000000002-200002-22-20000000000000000
χ774-4-440044-400-4-4-44004004000000-40000-44000000000000000000000000000-220000-22-220000000000000000
χ784-4-4400-242−2i32i3-42-442i3−2i3-200-20000002−2i32i32i3−2i32-20000000000000000000000000002-20000−1−i31+i3−1+i31−i30000000000000000
χ794-4-4400-242−2i32i3-42-442i3−2i3-200-20000002−2i32i32i3−2i32-2000000000000000000000000000-2200001+i3−1−i31−i3−1+i30000000000000000
χ804-4-4400-2422i3−2i3-42-44−2i32i3-200-200000022i3−2i3−2i32i32-20000000000000000000000000002-20000−1+i31−i3−1−i31+i30000000000000000
χ814-4-4400-2422i3−2i3-42-44−2i32i3-200-200000022i3−2i3−2i32i32-2000000000000000000000000000-2200001−i3−1+i31+i3−1−i30000000000000000
χ828-88-8008-4-80048-4400-800-400000040000-4400000000000000000000000000000000000000000000000000000
χ838-88-800-4-44−4i34i34-4-44−4i34i34002000000-22i3−2i32i3−2i32-200000000000000000000000000000000000000000000000000000
χ848-88-800-4-444i3−4i34-4-444i3−4i34002000000-2−2i32i3−2i32i32-200000000000000000000000000000000000000000000000000000
χ858-8-88008-4-8004-84-400800-4000000400004-400000000000000000000000000000000000000000000000000000
χ868-8-8800-4-44−4i34i3444-44i3−4i3-4002000000-22i3−2i3−2i32i3-2200000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444i3−4i3444-4−4i34i3-4002000000-2−2i32i32i3−2i3-2200000000000000000000000000000000000000000000000000000

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