Finite Group Databasebeta

← Group #11778223

Character table — Group #11778223

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666666662234466666666612121212466666666121212121212121212121212121244448888121212121212121224242424242424242244
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
χ5111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11-11-1
χ6111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-11
χ7111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-11
χ8111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1
χ9222222222222222222222-2-2222222222-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222222-2-22-2-2222222222-2-2-2-22-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000
χ112222222-1222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-1222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-1222-12-1-122222-1-2-2-1-1-1-1-1-1-1-1-11111-222-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−30000
χ142222222-1222-12-1-122222-1-2-2-1-1-1-1-1-1-1-1-11111-222-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−3330000
χ152222222-1222-12-1-1222-2-2-122-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-21122-1-1-1-11111000022-2-200000000-1-1-1-111110000
χ162222222-1222-12-1-1222-2-2-122-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-21122-1-1-1-111110000-2-222000000001111-1-1-1-10000
χ172222222-1222-12-1-1222-2-2-1-2-2-1-1-1-1-1-1-1-1-111112-2-211111122-1-1-2-21111-1-1-1-1000000000000000033−3−3−3−3330000
χ182222222-1222-12-1-1222-2-2-1-2-2-1-1-1-1-1-1-1-1-111112-2-211111122-1-1-2-21111-1-1-1-10000000000000000−3−33333−3−30000
χ19222222-12-1-1-12-122-1-1-122-12222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-1-1-12-122-1-1-122-12222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-1-1-12-122-1-1-122-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-1-122-1-1-1-111-2-2111111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-1-1-12-122-1-1-122-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-1-122-1-1-1-111-2-2111111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-1-1-12-122-1-1-1-2-2-12222-1-1-1-1-1-1-12222-211-2-2111111-2-2-1-1-1-1-1-1111122-2-200001111-1-1-1-1000000000000
χ24222222-12-1-1-12-122-1-1-1-2-2-12222-1-1-1-1-1-1-12222-211-2-2111111-2-2-1-1-1-1-1-11111-2-2220000-1-1-1-11111000000000000
χ25222222-12-1-1-12-122-1-1-1-2-2-1-2-222-1-1-1-1-1-1-1-2-2-2-2211-2-21111-1-122111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ26222222-12-1-1-12-122-1-1-1-2-2-1-2-222-1-1-1-1-1-1-1-2-2-2-2211-2-21111-1-122111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ272222-2-2222-2-22222-2-220022-2-2-22-2-2-2-22222-2-200000000000002-222-2-2000000000000000000000000000020-20
χ282222-2-2222-2-22222-2-220022-2-2-22-2-2-2-22222-2-200000000000002-222-2-20000000000000000000000000000-2020
χ292222-2-2222-2-22222-2-22002-22-2-22-2-2-2-222-2-2220000000000000-22-2-2220000000000000000000000000000020-2
χ302222-2-2222-2-22222-2-22002-22-2-22-2-2-2-222-2-2220000000000000-22-2-22200000000000000000000000000000-202
χ312-2-222-2222222-2-2-2-2-2-22-22002-2222-2-2-2-2000002-22-222-2-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i20000
χ322-2-222-2222222-2-2-2-2-2-22-22002-2222-2-2-2-2000002-22-222-2-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i20000
χ332-2-222-2222222-2-2-2-2-2-2-222002-2222-2-2-2-200000-22-22-2-222000000000000000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i20000
χ342-2-222-2222222-2-2-2-2-2-2-222002-2222-2-2-2-200000-22-22-2-222000000000000000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i20000
χ352-2-222-22-1222-1-211-2-2-22-2-100-11-1-1-111113−33−302-2-11-1-111003−3003−33−333−3−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ362-2-222-22-1222-1-211-2-2-22-2-100-11-1-1-111113−33−302-2-11-1-111003−3003−33−333−3−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ372-2-222-22-1222-1-211-2-2-22-2-100-11-1-1-11111−33−3302-2-11-1-11100−3300−33−33−3−3330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ382-2-222-22-1222-1-211-2-2-22-2-100-11-1-1-11111−33−3302-2-11-1-11100−3300−33−33−3−3330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ392-2-222-22-1222-1-211-2-2-2-22-100-11-1-1-111113−33−30-221-111-1-100−33003−33−3−3−3330000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ402-2-222-22-1222-1-211-2-2-2-22-100-11-1-1-111113−33−30-221-111-1-100−33003−33−3−3−3330000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ412-2-222-22-1222-1-211-2-2-2-22-100-11-1-1-11111−33−330-221-111-1-1003−300−33−3333−3−30000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ422-2-222-22-1222-1-211-2-2-2-22-100-11-1-1-11111−33−330-221-111-1-1003−300−33−3333−3−30000i2−i2−i2i200000000−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
χ45444444-2-2-2-2-2-2-2-2-2-2-2-2-4-4144-2-21111111-2-2-2-2-42222-1-1-1-12222-2-21111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-2-4-41-4-4-2-21111111222242222-1-1-1-1-2-2-2-222-1-1-1-111110000000000000000000000000000
χ474444-4-44-24-4-4-24-2-2-4-4400-24-422-22222-2-2-2-22200000000000004-4-2-22200000000000000000000000000000000
χ484444-4-44-24-4-4-24-2-2-4-4400-2-4422-22222-2-222-2-20000000000000-4422-2-200000000000000000000000000000000
χ494444-4-4-24-2224-24422-200-24-4-4-4-22222-2-244-4-40000000000000-22-2-22200000000000000000000000000000000
χ504444-4-4-24-2224-24422-200-2-44-4-4-22222-2-2-4-44400000000000002-222-2-200000000000000000000000000000000
χ514444-4-4-2-2-222-2-2-2-222-20014-4221-1-1-1-111-2-222000003-33-30000-2211-1-13-33-30000000000000000000000000000
χ524444-4-4-2-2-222-2-2-2-222-20014-4221-1-1-1-111-2-22200000-33-330000-2211-1-1-33-330000000000000000000000000000
χ534444-4-4-2-2-222-2-2-2-222-2001-44221-1-1-1-11122-2-2000003-33-300002-2-1-111-33-330000000000000000000000000000
χ544444-4-4-2-2-222-2-2-2-222-2001-44221-1-1-1-11122-2-200000-33-3300002-2-1-1113-33-30000000000000000000000000000
χ5544-4-40044-400-444-400-40040000-400004-4000000000000000000000000000002i−2i00002i−2i2i−2i0000000000000000
χ5644-4-40044-400-444-400-40040000-400004-400000000000000000000000000000−2i2i0000−2i2i−2i2i0000000000000000
χ5744-4-400-242−2i32i3-4-24-4−2i32i3200-200002−2i32i3−2i32i3-22000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ220000000000000000
χ5844-4-400-242−2i32i3-4-24-4−2i32i3200-200002−2i32i3−2i32i3-2200000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ220000000000000000
χ5944-4-400-2422i3−2i3-4-24-42i3−2i3200-2000022i3−2i32i3−2i3-22000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ140000000000000000
χ6044-4-400-2422i3−2i3-4-24-42i3−2i3200-2000022i3−2i32i3−2i3-2200000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ140000000000000000
χ614-44-40044-400-4-4-440040040000-40000-440000000000000000000000000002-200000000002-22-2000000000000
χ624-44-40044-400-4-4-440040040000-40000-44000000000000000000000000000-220000000000-22-22000000000000
χ634-44-400-242−2i32i3-42-442i3−2i3-200-200002−2i32i32i3−2i32-20000000000000000000000000002-20000000000−1+i31−i3−1−i31+i3000000000000
χ644-44-400-242−2i32i3-42-442i3−2i3-200-200002−2i32i32i3−2i32-2000000000000000000000000000-2200000000001−i3−1+i31+i3−1−i3000000000000
χ654-44-400-2422i3−2i3-42-44−2i32i3-200-2000022i3−2i3−2i32i32-20000000000000000000000000002-20000000000−1−i31+i3−1+i31−i3000000000000
χ664-44-400-2422i3−2i3-42-44−2i32i3-200-2000022i3−2i3−2i32i32-2000000000000000000000000000-2200000000001+i3−1−i31−i3−1+i3000000000000
χ674-4-444-4-24-2-2-242-4-42224-4-2004-4-2-2-2222200000-224-4-2-222000000000000000000000000000000000000000000
χ684-4-444-4-24-2-2-242-4-4222-44-2004-4-2-2-22222000002-2-4422-2-2000000000000000000000000000000000000000000
χ694-4-444-4-2-2-2-2-2-22222224-4100-22111-1-1-1-123−2323−230-22-2211-1-10023−2300−33−33−3−3330000000000000000000000000000
χ704-4-444-4-2-2-2-2-2-22222224-4100-22111-1-1-1-1−2323−23230-22-2211-1-100−2323003−33−333−3−30000000000000000000000000000
χ714-4-444-4-2-2-2-2-2-2222222-44100-22111-1-1-1-123−2323−2302-22-2-1-11100−232300−33−3333−3−30000000000000000000000000000
χ724-4-444-4-2-2-2-2-2-2222222-44100-22111-1-1-1-1−2323−232302-22-2-1-1110023−23003−33−3−3−3330000000000000000000000000000
χ734-4-44-44444-4-44-4-4-444-400400-444-4-444-4-40000000000000000000000000000000000000000000000000000000
χ744-4-44-444-24-4-4-2-42244-400-2002-2-222-2-22223−23−232300000000000000023−23−232300000000000000000000000000000000
χ754-4-44-444-24-4-4-2-42244-400-2002-2-222-2-222−232323−23000000000000000−232323−2300000000000000000000000000000000
χ764-4-44-44-24-22242-4-4-2-2200-200-44-222-2-222000000000000023−230000000023−23−23230000000000000000000000000000
χ774-4-44-44-24-22242-4-4-2-2200-200-44-222-2-2220000000000000−232300000000−232323−230000000000000000000000000000
χ784-4-44-44-2-2-222-2222-2-22001002-21-1-111-1-123−23−2323000003-3-33−23230000−333−33−3−330000000000000000000000000000
χ794-4-44-44-2-2-222-2222-2-22001002-21-1-111-1-123−23−232300000-333-323−230000−333−3−333−30000000000000000000000000000
χ804-4-44-44-2-2-222-2222-2-22001002-21-1-111-1-1−232323−23000003-3-3323−2300003−3−33−333−30000000000000000000000000000
χ814-4-44-44-2-2-222-2222-2-22001002-21-1-111-1-1−232323−2300000-333-3−232300003−3−333−3−330000000000000000000000000000
χ8288-8-8008-4-80048-4400-800-4000040000-440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-44−4i34i34-4-44−4i34i340020000-22i3−2i32i3−2i32-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-444i3−4i34-4-444i3−4i340020000-2−2i32i3−2i32i32-20000000000000000000000000000000000000000000000000000000
χ858-88-8008-4-8004-84-400800-40000400004-40000000000000000000000000000000000000000000000000000000
χ868-88-800-4-44−4i34i3444-44i3−4i3-40020000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ878-88-800-4-444i3−4i3444-4−4i34i3-40020000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000

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