Finite Group Databasebeta

← Group #11771807

Character table — Group #11771807

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666666662234466666666612121212466666666121212121212121212121212121244448888121212121212121224242424242424244444
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
χ5111111111111111111-1-11-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1ii−i−i-1-1-1-11111iiii−i−i−i−iii−i−i
χ6111111111111111111-1-11-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii
χ7111111111111111111-1-11-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii
χ8111111111111111111-1-11-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−i
χ9222222222222222222222-2-2222222222-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000
χ112222222-122-122-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-122-122-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-122-122-1-122222-1-2-2-1-1-1-1-1-1-1-1-11111-222-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−30000
χ142222222-122-122-1-122222-1-2-2-1-1-1-1-1-1-1-1-11111-222-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−3330000
χ152222222-122-122-1-1222-2-2-122-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-211221111-1-1-1-10000000000000000−i3−i3i3i3i3i3−i3−i30000
χ162222222-122-122-1-1222-2-2-122-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-211221111-1-1-1-10000000000000000i3i3−i3−i3−i3−i3i3i30000
χ172222222-122-122-1-1222-2-2-1-2-2-1-1-1-1-1-1-1-1-111112-2-211111122-1-1-2-2-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii0000
χ182222222-122-122-1-1222-2-2-1-2-2-1-1-1-1-1-1-1-1-111112-2-211111122-1-1-2-2-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i0000
χ19222222-12-1-12-1-122-1-1-122-12222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-1-12-1-122-1-1-122-12222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-1-12-1-122-1-1-122-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-1-122-1-1-1-111-2-2111111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-1-12-1-122-1-1-122-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-1-122-1-1-1-111-2-2111111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-1-12-1-122-1-1-1-2-2-12222-1-1-1-1-1-1-12222-211-2-2111111-2-2-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ24222222-12-1-12-1-122-1-1-1-2-2-12222-1-1-1-1-1-1-12222-211-2-2111111-2-2-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ25222222-12-1-12-1-122-1-1-1-2-2-1-2-222-1-1-1-1-1-1-1-2-2-2-2211-2-21111-1-12211-1-1-1-1111122-2-200001111-1-1-1-1000000000000
χ26222222-12-1-12-1-122-1-1-1-2-2-1-2-222-1-1-1-1-1-1-1-2-2-2-2211-2-21111-1-12211-1-1-1-11111-2-2220000-1-1-1-11111000000000000
χ272-2-222-222222-2-2-2-2-2-220022i−2i2-2222-2-2-2-22i2i−2i−2i00000000000002i−2i00002i2i−2i−2i0000000000000000000000001+i−1−i1−i−1+i
χ282-2-222-222222-2-2-2-2-2-220022i−2i2-2222-2-2-2-22i2i−2i−2i00000000000002i−2i00002i2i−2i−2i000000000000000000000000−1−i1+i−1+i1−i
χ292-2-222-222222-2-2-2-2-2-22002−2i2i2-2222-2-2-2-2−2i−2i2i2i0000000000000−2i2i0000−2i−2i2i2i0000000000000000000000001−i−1+i1+i−1−i
χ302-2-222-222222-2-2-2-2-2-22002−2i2i2-2222-2-2-2-2−2i−2i2i2i0000000000000−2i2i0000−2i−2i2i2i000000000000000000000000−1+i1−i−1−i1+i
χ312-2-22-2222-2-22-2-2-2-22222-2200-222-2-222-2-2000002-22-222-2-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i20000
χ322-2-22-2222-2-22-2-2-2-22222-2200-222-2-222-2-2000002-22-222-2-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i20000
χ332-2-22-2222-2-22-2-2-2-2222-22200-222-2-222-2-200000-22-22-2-2220000000000000000002−2−22000000002−22−2−22−220000
χ342-2-22-2222-2-22-2-2-2-2222-22200-222-2-222-2-200000-22-22-2-222000000000000000000−222−200000000−22−222−22−20000
χ352-2-22-222-1-2-2-1-2-2112222-2-1001-1-111-1-1113−33−302-2-11-1-111003−30033−3−33−33−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ362-2-22-222-1-2-2-1-2-2112222-2-1001-1-111-1-1113−33−302-2-11-1-111003−30033−3−33−33−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ372-2-22-222-1-2-2-1-2-2112222-2-1001-1-111-1-111−33−3302-2-11-1-11100−3300−3−333−33−330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ382-2-22-222-1-2-2-1-2-2112222-2-1001-1-111-1-111−33−3302-2-11-1-11100−3300−3−333−33−330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ392-2-22-222-1-2-2-1-2-211222-22-1001-1-111-1-1113−33−30-221-111-1-100−3300−3−3333−33−300002−2−2200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ402-2-22-222-1-2-2-1-2-211222-22-1001-1-111-1-1113−33−30-221-111-1-100−3300−3−3333−33−30000−222−200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ412-2-22-222-1-2-2-1-2-211222-22-1001-1-111-1-111−33−330-221-111-1-1003−30033−3−3−33−3300002−2−2200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ422-2-22-222-1-2-2-1-2-211222-22-1001-1-111-1-111−33−330-221-111-1-1003−30033−3−3−33−330000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ43444444-2-2-2-2-2-2-2-2-2-2-2-244144-2-21111111-2-2-2-24-2-2-2-21111-2-2-2-2-2-2111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2441-4-4-2-211111112222-4-2-2-2-21111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-2-4-4144-2-21111111-2-2-2-2-42222-1-1-1-12222-2-2-1-1-1-111110000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-2-4-41-4-4-2-21111111222242222-1-1-1-1-2-2-2-2221111-1-1-1-10000000000000000000000000000
χ474444-4-444-4-444444-4-4400400-4-44-4-4-4-4440000000000000000000000000000000000000000000000000000000
χ484444-4-44-2-4-4-244-2-2-4-4400-20022-22222-2-2−2i32i32i3−2i30000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ494444-4-44-2-4-4-244-2-2-4-4400-20022-22222-2-22i3−2i3−2i32i300000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ504444-4-4-24224-2-24422-200-200-4-4-22222-2-20000000000000−2i32i30000−2i32i3−2i32i300000000000000000000000000000000
χ514444-4-4-24224-2-24422-200-200-4-4-22222-2-200000000000002i3−2i300002i3−2i32i3−2i300000000000000000000000000000000
χ524444-4-4-2-222-2-2-2-2-222-200100221-1-1-1-111−2i32i32i3−2i3000003-33-3−2i32i30000i3−i3i3−i3i3−i3−i3i30000000000000000000000000000
χ534444-4-4-2-222-2-2-2-2-222-200100221-1-1-1-111−2i32i32i3−2i300000-33-332i3−2i30000−i3i3−i3i3i3−i3−i3i30000000000000000000000000000
χ544444-4-4-2-222-2-2-2-2-222-200100221-1-1-1-1112i3−2i3−2i32i3000003-33-32i3−2i30000−i3i3−i3i3−i3i3i3−i30000000000000000000000000000
χ554444-4-4-2-222-2-2-2-2-222-200100221-1-1-1-1112i3−2i3−2i32i300000-33-33−2i32i30000i3−i3i3−i3−i3i3i3−i30000000000000000000000000000
χ5644-4-4004400-44-44-400-40040000-400004-4000000000000000000000000000002i−2i00002i−2i2i−2i0000000000000000
χ5744-4-4004400-44-44-400-40040000-400004-400000000000000000000000000000−2i2i0000−2i2i−2i2i0000000000000000
χ5844-4-400-24−2i32i3-4-224-4−2i32i3200-200002−2i32i3−2i32i3-22000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ220000000000000000
χ5944-4-400-24−2i32i3-4-224-4−2i32i3200-200002−2i32i3−2i32i3-2200000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ220000000000000000
χ6044-4-400-242i3−2i3-4-224-42i3−2i3200-2000022i3−2i32i3−2i3-22000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ140000000000000000
χ6144-4-400-242i3−2i3-4-224-42i3−2i3200-2000022i3−2i32i3−2i3-2200000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ140000000000000000
χ624-44-4004400-4-44-4400-40040000-40000-440000000000000000000000000002i−2i00000000002i−2i2i−2i000000000000
χ634-44-4004400-4-44-4400-40040000-40000-44000000000000000000000000000−2i2i0000000000−2i2i−2i2i000000000000
χ644-44-400-24−2i32i3-42-2-442i3−2i3200-200002−2i32i32i3−2i32-20000000000000000000000000002i−2i00000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ654-44-400-24−2i32i3-42-2-442i3−2i3200-200002−2i32i32i3−2i32-2000000000000000000000000000−2i2i0000000000−2ζ222ζ22−2ζ142ζ14000000000000
χ664-44-400-242i3−2i3-42-2-44−2i32i3200-2000022i3−2i3−2i32i32-20000000000000000000000000002i−2i00000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ674-44-400-242i3−2i3-42-2-44−2i32i3200-2000022i3−2i3−2i32i32-2000000000000000000000000000−2i2i0000000000−2ζ142ζ14−2ζ222ζ22000000000000
χ684-4-444-44-244-2-4-422-4-4400-24i−4i-22-2-2-22222−2i−2i2i2i00000000000004i−4i0000−2i−2i2i2i0000000000000000000000000000
χ694-4-444-44-244-2-4-422-4-4400-2−4i4i-22-2-2-222222i2i−2i−2i0000000000000−4i4i00002i2i−2i−2i0000000000000000000000000000
χ704-4-444-4-24-2-2422-4-422-200-24i−4i4-4-2-2-222224i4i−4i−4i0000000000000−2i2i0000−2i−2i2i2i0000000000000000000000000000
χ714-4-444-4-24-2-2422-4-422-200-2−4i4i4-4-2-2-22222−4i−4i4i4i00000000000002i−2i00002i2i−2i−2i0000000000000000000000000000
χ724-4-444-4-2-2-2-2-2222222-20014i−4i-22111-1-1-1-1−2i−2i2i2i000003-3-330000−2i2i−3i3i3i−3iii−i−i0000000000000000000000000000
χ734-4-444-4-2-2-2-2-2222222-20014i−4i-22111-1-1-1-1−2i−2i2i2i00000-333-30000−2i2i3i−3i−3i3iii−i−i0000000000000000000000000000
χ744-4-444-4-2-2-2-2-2222222-2001−4i4i-22111-1-1-1-12i2i−2i−2i000003-3-3300002i−2i3i−3i−3i3i−i−iii0000000000000000000000000000
χ754-4-444-4-2-2-2-2-2222222-2001−4i4i-22111-1-1-1-12i2i−2i−2i00000-333-300002i−2i−3i3i3i−3i−i−iii0000000000000000000000000000
χ764-4-44-44-2422422-4-4-2-2-24-4-200-44-222-2-22200000-224-4-2-222000000000000000000000000000000000000000000
χ774-4-44-44-2422422-4-4-2-2-2-44-200-44-222-2-222000002-2-4422-2-2000000000000000000000000000000000000000000
χ784-4-44-44-2-222-22222-2-2-24-41002-21-1-111-1-123−2323−230-22-2211-1-10023−2300−3−333−33−330000000000000000000000000000
χ794-4-44-44-2-222-22222-2-2-24-41002-21-1-111-1-1−2323−23230-22-2211-1-100−23230033−3−33−33−30000000000000000000000000000
χ804-4-44-44-2-222-22222-2-2-2-441002-21-1-111-1-123−2323−2302-22-2-1-11100−23230033−3−3−33−330000000000000000000000000000
χ814-4-44-44-2-222-22222-2-2-2-441002-21-1-111-1-1−2323−232302-22-2-1-1110023−2300−3−3333−33−30000000000000000000000000000
χ8288-8-8008-40048-8-4400-800-4000040000-440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4−4i34i34-44-44−4i34i340020000-22i3−2i32i3−2i32-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-44i3−4i34-44-444i3−4i340020000-2−2i32i3−2i32i32-20000000000000000000000000000000000000000000000000000000
χ858-88-8008-4004-884-400-800-40000400004-40000000000000000000000000000000000000000000000000000000
χ868-88-800-4-4−4i34i344-44-44i3−4i340020000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ878-88-800-4-44i3−4i344-44-4−4i34i340020000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000

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