Finite Group Databasebeta

← Group #72231060

Character table — Group #72231060

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122244444444444446688888888888888888888888888888824242424242424242424242425255050505050505075757575100100100100100150150150150
order1223655555561010101010102410101010101015151515151530303030303030303030303030303030303010101010101020202020202022244446644446121212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1i−ii−i-1-1ii−i−i-1ii−i−i-1-1i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1−ii−ii-1-1−i−iii-1−i−iii-1-1−ii
χ5111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-1
χ6111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-111
χ7111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i-1-1−i−iii-1ii−i−i11−ii
χ8111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii-1-1ii−i−i-1−i−iii11i−i
χ911-111111111-11111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-111-1-111-1-1-1-1-11-11-11-111
χ1011-111111111-11111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-111111111-1-11-111-1-1-1
χ1111-111111111-11111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11i−i−ii-1-1−i−iii1i−i−ii-11i−i
χ1211-111111111-11111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11−iii−i-1-1ii−i−i1−iii−i-11−ii
χ1311-111111111-1111111-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1111111-11-11-1-11-1-1
χ1411-111111111-1111111-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-11-11-1111
χ1511-111111111-1111111-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11i−i−ii-1-1ii−i−i1i−i−ii1-1−ii
χ1611-111111111-1111111-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11−iii−i-1-1−i−iii1−iii−i1-1i−i
χ17222-1-1222222-122222200222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002222222-1-10000-1-1-1-1-10000
χ18222-1-1222222-122222200222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-2-2-2-2-1-10000-111110000
χ19222-1-1222222-122222200222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-22i−2i2i−2i1100001−i−iii0000
χ20222-1-1222222-122222200222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2−2i2i−2i2i1100001ii−i−i0000
χ2122-2-1-1222222122222200-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000022-222-2-2-1-100001-11-110000
χ2222-2-1-1222222122222200-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000022-2-2-222-1-1000011-11-10000
χ2322-2-1-1222222122222200-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000-2-222i−2i−2i2i110000-1−iii−i0000
χ2422-2-1-1222222122222200-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000-2-22−2i2i2i−2i110000-1i−i−ii0000
χ252-202-22222220-2-2-2-2-2-200000000222222-2-2-2-2-2-20000000000000000000000002-2000002-22i−2i2i−2i000000000
χ262-202-22222220-2-2-2-2-2-200000000222222-2-2-2-2-2-20000000000000000000000002-2000002-2−2i2i−2i2i000000000
χ272-202-22222220-2-2-2-2-2-200000000222222-2-2-2-2-2-2000000000000000000000000-2200000-222-2-22000000000
χ282-202-22222220-2-2-2-2-2-200000000222222-2-2-2-2-2-2000000000000000000000000-2200000-22-222-2000000000
χ29444444-1-1-1-1-144-1-1-1-1-1444-1-1-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-10000000000000000000000
χ30444444-1-1-1-1-144-1-1-1-1-1-4-44-1-1-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-411111-4111110000000000000000000000
χ3144444-14-1-1-1-14-14-1-1-1-144-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-10000000000000000000000
χ3244444-14-1-1-1-14-14-1-1-1-1-4-4-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-11-411111-411110000000000000000000000
χ3344444-1-1−1−53+523−52−1+54-1-1−1−53+523−52−1+544-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+50000000000000000000000
χ3444444-1-1−1−53+523−52−1+54-1-1−1−53+523−52−1+5-4-4-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5111+5−3−52−3+521−5111+5−3−52−3+521−50000000000000000000000
χ3544444-1-13+52−1+5−1−53−524-1-13+52−1+5−1−53−5244-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−520000000000000000000000
χ3644444-1-13+52−1+5−1−53−524-1-13+52−1+5−1−53−52-4-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−5211−3−521−51+5−3+5211−3−521−51+5−3+520000000000000000000000
χ3744444-1-13−52−1−5−1+53+524-1-13−52−1−5−1+53+5244-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+520000000000000000000000
χ3844444-1-13−52−1−5−1+53+524-1-13−52−1−5−1+53+52-4-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+5211−3+521+51−5−3−5211−3+521+51−5−3−520000000000000000000000
χ3944444-1-1−1+53−523+52−1−54-1-1−1+53−523+52−1−544-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−50000000000000000000000
χ4044444-1-1−1+53−523+52−1−54-1-1−1+53−523+52−1−5-4-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5111−5−3+52−3−521+5111−5−3+52−3−521+50000000000000000000000
χ4144-4444-1-1-1-1-1-44-1-1-1-1-14-4-4111114-1-1-1-1-14-1-1-1-1-1-4-411111111114-1-1-1-1-1-4111110000000000000000000000
χ4244-4444-1-1-1-1-1-44-1-1-1-1-1-44-4111114-1-1-1-1-14-1-1-1-1-1-4-41111111111-4111114-1-1-1-1-10000000000000000000000
χ4344-444-14-1-1-1-1-4-14-1-1-1-14-41-41111-14-1-1-1-1-14-1-1-1-111-4-411111111-14-1-1-1-11-411110000000000000000000000
χ4444-444-14-1-1-1-1-4-14-1-1-1-1-441-41111-14-1-1-1-1-14-1-1-1-111-4-4111111111-41111-14-1-1-1-10000000000000000000000
χ4544-444-1-1−1−53+523−52−1+5-4-1-1−1−53+523−52−1+54-4111+5−3−52−3+521−5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+511111+51+5−3−52−3−52−3+52−3+521−51−5-1-1−1−53+523−52−1+5111+5−3−52−3+521−50000000000000000000000
χ4644-444-1-1−1−53+523−52−1+5-4-1-1−1−53+523−52−1+5-44111+5−3−52−3+521−5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+511111+51+5−3−52−3−52−3+52−3+521−51−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+50000000000000000000000
χ4744-444-1-13+52−1+5−1−53−52-4-1-13+52−1+5−1−53−524-411−3−521−51+5−3+52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+52-1-13+52−1+5−1−53−5211−3−521−51+5−3+520000000000000000000000
χ4844-444-1-13+52−1+5−1−53−52-4-1-13+52−1+5−1−53−52-4411−3−521−51+5−3+52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−520000000000000000000000
χ4944-444-1-13−52−1−5−1+53+52-4-1-13−52−1−5−1+53+524-411−3+521+51−5−3−52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−52-1-13−52−1−5−1+53+5211−3+521+51−5−3−520000000000000000000000
χ5044-444-1-13−52−1−5−1+53+52-4-1-13−52−1−5−1+53+52-4411−3+521+51−5−3−52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+520000000000000000000000
χ5144-444-1-1−1+53−523+52−1−5-4-1-1−1+53−523+52−1−54-4111−5−3+52−3−521+5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+5-1-1−1+53−523+52−1−5111−5−3+52−3−521+50000000000000000000000
χ5244-444-1-1−1+53−523+52−1−5-4-1-1−1+53−523+52−1−5-44111−5−3+52−3−521+5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−50000000000000000000000
χ534-40-224444440-4-4-4-4-4-400000000-2-2-2-2-2-22222220000000000000000000000004-400000-220000000000000
χ544-40-224444440-4-4-4-4-4-400000000-2-2-2-2-2-2222222000000000000000000000000-44000002-20000000000000
χ55888-4-48-2-2-2-2-2-48-2-2-2-2-2008-2-2-2-2-2-411111-411111-4-411111111110000000000000000000000000000000000
χ56888-4-4-28-2-2-2-2-4-28-2-2-2-200-28-2-2-2-21-411111-4111111-4-4111111110000000000000000000000000000000000
χ57888-4-4-2-2−2−253+53−5−2+25-4-2-2−2−253+53−5−2+2500-2-2−2−253+53−5−2+25111+5−3−52−3+521−5111+5−3−52−3+521−511111+51+5−3−52−3−52−3+52−3+521−51−50000000000000000000000000000000000
χ58888-4-4-2-23+5−2+25−2−253−5-4-2-23+5−2+25−2−253−500-2-23+5−2+25−2−253−511−3−521−51+5−3+5211−3−521−51+5−3+521111−3−52−3−521−51−51+51+5−3+52−3+520000000000000000000000000000000000
χ59888-4-4-2-23−5−2−25−2+253+5-4-2-23−5−2−25−2+253+500-2-23−5−2−25−2+253+511−3+521+51−5−3−5211−3+521+51−5−3−521111−3+52−3+521+51+51−51−5−3−52−3−520000000000000000000000000000000000
χ60888-4-4-2-2−2+253−53+5−2−25-4-2-2−2+253−53+5−2−2500-2-2−2+253−53+5−2−25111−5−3+52−3−521+5111−5−3+52−3−521+511111−51−5−3+52−3+52−3−52−3−521+51+50000000000000000000000000000000000
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χ6488-8-4-4-2-23+5−2+25−2−253−54-2-23+5−2+25−2−253−50022−3−52−252+25−3+511−3−521−51+5−3+5211−3−521−51+5−3+52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−520000000000000000000000000000000000
χ6588-8-4-4-2-23−5−2−25−2+253+54-2-23−5−2−25−2+253+50022−3+52+252−25−3−511−3+521+51−5−3−5211−3+521+51−5−3−52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+520000000000000000000000000000000000
χ6688-8-4-4-2-2−2+253−53+5−2−254-2-2−2+253−53+5−2−2500222−25−3+5−3−52+25111−5−3+52−3−521+5111−5−3+52−3−521+5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−50000000000000000000000000000000000
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χ708-808-8-2-23+5−2+25−2−253−5022−3−52−252+25−3+500000000-2-23+5−2+25−2−253−522−3−52−252+25−3+50000000000000000000000000000000000000000000000
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χ728-808-8-2-2−2+253−53+5−2−250222−25−3+5−3−52+2500000000-2-2−2+253−53+5−2−25222−25−3+5−3−52+250000000000000000000000000000000000000000000000
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χ778-80-44-2-2−2−253+53−5−2+250222+25−3−5−3+52−2500000000111+5−3−52−3+521−5-1-1−1−53+523−52−1+5−i15i15i15−i15003ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ58−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ58−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ582ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ58000000000000000000000000000000000000
χ788-80-44-2-2−2−253+53−5−2+250222+25−3−5−3+52−2500000000111+5−3−52−3+521−5-1-1−1−53+523−52−1+5i15−i15−i15i1500−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ583ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ582ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ58−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ58000000000000000000000000000000000000
χ798-80-44-2-23+5−2+25−2−253−5022−3−52−252+25−3+50000000011−3−521−51+5−3+52-1-13+52−1+5−1−53−52−i15i15−i15i15−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ583ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ5800002ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ58−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ580000000000000000000000000000000000
χ808-80-44-2-23+5−2+25−2−253−5022−3−52−252+25−3+50000000011−3−521−51+5−3+52-1-13+52−1+5−1−53−52i15−i15i15−i153ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ58−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ580000−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ582ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ580000000000000000000000000000000000
χ818-80-44-2-23−5−2−25−2+253+5022−3+52+252−25−3−50000000011−3+521+51−5−3−52-1-13−52−1−5−1+53+52−i15i15−i15i152ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ58−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ580000−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ583ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ580000000000000000000000000000000000
χ828-80-44-2-23−5−2−25−2+253+5022−3+52+252−25−3−50000000011−3+521+51−5−3−52-1-13−52−1−5−1+53+52i15−i15i15−i15−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ582ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ5800003ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ58−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ580000000000000000000000000000000000
χ838-80-44-2-2−2+253−53+5−2−250222−25−3+5−3−52+2500000000111−5−3+52−3−521+5-1-1−1+53−523+52−1−5−i15i15i15−i1500−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ582ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ583ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ58−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ58000000000000000000000000000000000000
χ848-80-44-2-2−2+253−53+5−2−250222−25−3+5−3−52+2500000000111−5−3+52−3−521+5-1-1−1+53−523+52−1−5i15−i15−i15i15002ζ2+3ζ14−2ζ22+3ζ26−3ζ34+2ζ38−3ζ46−2ζ58−2ζ2−3ζ14+2ζ22−3ζ26+3ζ34−2ζ38+3ζ46+2ζ58−3ζ2−2ζ14+3ζ22−2ζ26+2ζ34−3ζ38+2ζ46+3ζ583ζ2+2ζ14−3ζ22+2ζ26−2ζ34+3ζ38−2ζ46−3ζ58000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.