Finite Group Databasebeta

← Group #11756911

Character table — Group #11756911

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size112222222444444666688888888881212121212121212161616161616161616161616161616303060606060606060
order12224551010101010102020244436151515153030303010102020202020206612303030303030303060606060882444888
χ11111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111-1-1111111-1-1-1-1-11-111111111111-1-11111-1-11-1-11111-1-1-1-1-1-1-1-111-111-11-1-1
χ4111-1-1111111-1-1-1-1-11-111111111111-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-111
χ511-11-11111-1-111-1-1-1-1111111111111-1-111-1-111-11-1-1-1-1-11111-1-1-1-111-11-11-11-1
χ611-11-11111-1-111-1-1-1-1111111111111-1-111-1-111-11-1-1-1-1-11111-1-1-1-1-1-11-11-11-11
χ711-1-111111-1-1-1-1111-1-1111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11
χ811-1-111111-1-1-1-1111-1-1111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1
χ92222222222222222222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000
χ1022222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000
χ1122222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222-1-1−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-1-1-1−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116000000000
χ1222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222-1-1−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-1-1-1−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76000000000
χ1322222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000
χ1422222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222-1-1−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-1-1-1−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68000000000
χ1522222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222-1-1−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-1-1-1−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92000000000
χ16222-2-2222222-2-2-2-2-22-22-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-111-1-1-1-111111111000000000
χ17222-2-2−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52-22-2222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−52−1−52−1+52−1−52−1+521+521−522-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000
χ18222-2-2−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52-22-22-1-1−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ1161+521−52−1−52−1+52−1−52−1+521+521−52-111−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116000000000
χ19222-2-2−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52-22-22-1-1−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ761+521−52−1−52−1+52−1−52−1+521+521−52-111−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76000000000
χ20222-2-2−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52-22-2222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1−521−521+522-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000
χ21222-2-2−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52-22-22-1-1−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ681−521+52−1+52−1−52−1+52−1−521−521+52-111−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68000000000
χ22222-2-2−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52-22-22-1-1−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ921−521+52−1+52−1−52−1+52−1−521−521+52-111−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92000000000
χ2322-22-22222-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-2-222-2-2221-111111-1-1-1-11111000000000
χ2422-22-2−1−52−1+52−1−52−1+521+521−52−1−52−1+521+521−52-2-22222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−52−1−52−1+521+521−52−1−52−1+52-22-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000
χ2522-22-2−1−52−1+52−1−52−1+521+521−52−1−52−1+521+521−52-2-222-1-1−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ1161+521−52−1−52−1+521+521−52−1−52−1+521-11ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116000000000
χ2622-22-2−1−52−1+52−1−52−1+521+521−52−1−52−1+521+521−52-2-222-1-1−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ761+521−52−1−52−1+521+521−52−1−52−1+521-11ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76000000000
χ2722-22-2−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521+52-2-22222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+52−1+52−1−52-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000
χ2822-22-2−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521+52-2-222-1-1−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ681−521+52−1+52−1−521−521+52−1+52−1−521-11ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68000000000
χ2922-22-2−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521+52-2-222-1-1−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ921−521+52−1+52−1−521−521+52−1+52−1−521-11ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92000000000
χ3022-2-222222-2-2-2-2222-2-22-1-1-1-1-1-1-1-1-1-12222-2-2-2-211-111111111-1-1-1-1000000000
χ3122-2-22−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+522-2-2222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521−521+521−52-2-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000
χ3222-2-22−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+522-2-22-1-1−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−1−52−1+52−1−52−1+521+521−521+521−5211-1ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116000000000
χ3322-2-22−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+522-2-22-1-1−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−1−52−1+52−1−52−1+521+521−521+521−5211-1ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76000000000
χ3422-2-22−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−522-2-2222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521+521−521+52-2-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000
χ3522-2-22−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−522-2-22-1-1−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−1+52−1−52−1+52−1−521−521+521−521+5211-1ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68000000000
χ3622-2-22−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−522-2-22-1-1−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−1+52−1−52−1+52−1−521−521+521−521+5211-1ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92000000000
χ37333333333333333-1-1-1-10000000000-1-1-1-1-1-1-1-100000000000000011-1-1-1-1111
χ38333333333333333-1-1-1-10000000000-1-1-1-1-1-1-1-1000000000000000-1-11111-1-1-1
χ39333-3-3333333-3-3-3-31-11-1000000000011-1-1-1-111000000000000000111-1-111-1-1
χ40333-3-3333333-3-3-3-31-11-1000000000011-1-1-1-111000000000000000-1-1-111-1-111
χ4133-33-33333-3-333-3-311-1-1000000000011-1-111-1-1000000000000000111-11-1-11-1
χ4233-33-33333-3-333-3-311-1-1000000000011-1-111-1-1000000000000000-1-1-11-111-11
χ4333-3-333333-3-3-3-333-111-10000000000-1-1-1-1111100000000000000011-1-111-1-11
χ4433-3-333333-3-3-3-333-111-10000000000-1-1-1-11111000000000000000-1-111-1-111-1
χ454-400044-4-40000000000-22-2-2-2-222220000000000000000000000022−220000000
χ464-400044-4-40000000000-22-2-2-2-2222200000000000000000000000−22220000000
χ4766666−3−352−3+352−3−352−3+352−3−352−3+352−3−352−3+352−3−352−3+352-2-2-2-200000000001+521−521+521−521+521−521+521−52000000000000000000000000
χ4866666−3+352−3−352−3+352−3−352−3+352−3−352−3+352−3−352−3+352−3−352-2-2-2-200000000001−521+521−521+521−521+521−521+52000000000000000000000000
χ49666-6-6−3−352−3+352−3−352−3+352−3−352−3+3523+3523−3523+3523−3522-22-20000000000−1−52−1+521+521−521+521−52−1−52−1+52000000000000000000000000
χ50666-6-6−3+352−3−352−3+352−3−352−3+352−3−3523−3523+3523−3523+3522-22-20000000000−1+52−1−521−521+521−521+52−1+52−1−52000000000000000000000000
χ5166-66-6−3−352−3+352−3−352−3+3523+3523−352−3−352−3+3523+3523−35222-2-20000000000−1−52−1+521+521−52−1−52−1+521+521−52000000000000000000000000
χ5266-66-6−3+352−3−352−3+352−3−3523−3523+352−3+352−3−3523−3523+35222-2-20000000000−1+52−1−521−521+52−1+52−1−521−521+52000000000000000000000000
χ5366-6-66−3−352−3+352−3−352−3+3523+3523−3523+3523−352−3−352−3+352-222-200000000001+521−521+521−52−1−52−1+52−1−52−1+52000000000000000000000000
χ5466-6-66−3+352−3−352−3+352−3−3523−3523+3523−3523+352−3+352−3−352-222-200000000001−521+521−521+52−1+52−1−52−1+52−1−52000000000000000000000000
χ558-800088-8-800000000002-22222-2-2-2-200000000000000000000000000000000
χ568-8000−2−25−2+252+252−2500000000002-22ζ28+2ζ922ζ52+2ζ682ζ4+2ζ1162ζ44+2ζ76−2ζ28−2ζ92−2ζ52−2ζ68−2ζ4−2ζ116−2ζ44−2ζ7600000000000000000000000000000000
χ578-8000−2−25−2+252+252−2500000000002-22ζ52+2ζ682ζ28+2ζ922ζ44+2ζ762ζ4+2ζ116−2ζ52−2ζ68−2ζ28−2ζ92−2ζ44−2ζ76−2ζ4−2ζ11600000000000000000000000000000000
χ588-8000−2−25−2+252+252−250000000000-441+51+51−51−5−1−5−1−5−1+5−1+500000000000000000000000000000000
χ598-8000−2+25−2−252−252+2500000000002-22ζ44+2ζ762ζ4+2ζ1162ζ28+2ζ922ζ52+2ζ68−2ζ44−2ζ76−2ζ4−2ζ116−2ζ28−2ζ92−2ζ52−2ζ6800000000000000000000000000000000
χ608-8000−2+25−2−252−252+2500000000002-22ζ4+2ζ1162ζ44+2ζ762ζ52+2ζ682ζ28+2ζ92−2ζ4−2ζ116−2ζ44−2ζ76−2ζ52−2ζ68−2ζ28−2ζ9200000000000000000000000000000000
χ618-8000−2+25−2−252−252+250000000000-441−51−51+51+5−1+5−1+5−1−5−1−500000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1).