Finite Group Databasebeta

← Group #13087740

Character table — Group #13087740

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222222244444444444444444444444448888888888888888888888888888881515181830303030303636363636606060606060607272120
order12334556610103461212121215151515151515152020303030303030303012121212202060606060606060606060606060606060606060606060606022884668824040404024121212242410106
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-111111-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111-1-11
χ5111111111111-111-1-11111111111111111111-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-11-1-111-1-1-1
χ6111111111111-111-1-11111111111111111111-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-11-11-1-1-1-1111
χ7111111111111-111-1-11111111111111111111-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-111-1-1-1-11
χ8111111111111-111-1-11111111111111111111-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-1111111-1
χ922222−1−52−1+5222−1−52−1+522222222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522222−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+520022000002−1−52−1−52−1+52−1+520000000−1−52−1+520
χ1022222−1−52−1+5222−1−52−1+522222222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522222−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+5200-2-200000-21+521+521−521−5200000001+521−520
χ1122222−1−52−1+5222−1−52−1+522-222-2-22−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-22-2-21+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−52002200000-2−1−52−1−52−1+52−1+5200000001+521−520
χ1222222−1−52−1+5222−1−52−1+522-222-2-22−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-22-2-21+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−5200-2-20000021+521+521−521−520000000−1−52−1+520
χ1322222−1+52−1−5222−1+52−1−522222222−1+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+52−1−52−1−52−1−52−1−522222−1+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+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520022000002−1+52−1+52−1−52−1−520000000−1+52−1−520
χ1422222−1+52−1−5222−1+52−1−522222222−1+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+52−1−52−1−52−1−52−1−522222−1+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+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200-2-200000-21−521−521+521+5200000001−521+520
χ1522222−1+52−1−5222−1+52−1−522-222-2-22−1+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+52−1−52−1−52−1−52−1−52-22-2-21−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521−521−521−521−521+521+521+521+521+521+521+521+52002200000-2−1+52−1+52−1−52−1−5200000001−521+520
χ1622222−1+52−1−5222−1+52−1−522-222-2-22−1+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+52−1−52−1−52−1−52−1−52-22-2-21−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521−521−521−521−521+521+521+521+521+521+521+521+5200-2-20000021−521−521+521+520000000−1+52−1−520
χ172222-2222222202-200-222222222-2-2222222220-20000-2-2-2-2-2-2-2-200000000000000002200-222000000000-20000000
χ182222-2222222202-200-222222222-2-2222222220-20000-2-2-2-2-2-2-2-20000000000000000-2-2002-2-200000000020000000
χ19222-1222-1222-12-1222-12-1-1-12-1-1-1222-1-1-12-1-1-1-1-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000220000020000-1-100-1
χ20222-1222-1222-12-1222-12-1-1-12-1-1-1222-1-1-12-1-1-1-1-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000-2-200000-2000011001
χ21222-1222-1222-1-2-12-2-2-12-1-1-12-1-1-1222-1-1-12-1-1-11-111-2-22-1-1-12-1-1-1-2-2111111-2-211111100000002200000-20000-1-1001
χ22222-1222-1222-1-2-12-2-2-12-1-1-12-1-1-1222-1-1-12-1-1-11-111-2-22-1-1-12-1-1-1-2-2111111-2-21111110000000-2-200000200001100-1
χ2322-122222-122-12-1-1-1-12-12-1-1-12-1-122-12-1-1-12-1-12-1-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-122002-1-1000000002-1-1-100000
χ2422-122222-122-12-1-1-1-12-12-1-1-12-1-122-12-1-1-12-1-12-1-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-200-21100000000-211100000
χ2522-122222-122-1-2-1-1112-12-1-1-12-1-122-12-1-1-12-1-1-2-111-2-2-12-1-1-12-1-111-2-2111111-2-2111122002-1-100000000-2-11100000
χ2622-122222-122-1-2-1-1112-12-1-1-12-1-122-12-1-1-12-1-1-2-111-2-2-12-1-1-12-1-111-2-2111111-2-21111-2-200-2110000000021-1-100000
χ2722-12-2222-122-10-11−i3i3-2-12-1-1-12-1-1-2-2-12-1-1-12-1-101−i3i3001-2111-211−i3i300−i3−i3i3i3−i3i300−i3−i3i3i32200-2-1-10000000001−i3i300000
χ2822-12-2222-122-10-11−i3i3-2-12-1-1-12-1-1-2-2-12-1-1-12-1-101−i3i3001-2111-211−i3i300−i3−i3i3i3−i3i300−i3−i3i3i3-2-200211000000000-1i3−i300000
χ2922-12-2222-122-10-11i3−i3-2-12-1-1-12-1-1-2-2-12-1-1-12-1-101i3−i3001-2111-211i3−i300i3i3−i3−i3i3−i300i3i3−i3−i32200-2-1-10000000001i3−i300000
χ3022-12-2222-122-10-11i3−i3-2-12-1-1-12-1-1-2-2-12-1-1-12-1-101i3−i3001-2111-211i3−i300i3i3−i3−i3i3−i300i3i3−i3−i3-2-200211000000000-1−i3i300000
χ312-222022-2-2-2-220-200002222222200-2-2-2-2-2-2-2-20000000000000000000000000000002-2−i2i202-2−i2i20−i2i2−i2i200000−i2i2000
χ322-222022-2-2-2-220-200002222222200-2-2-2-2-2-2-2-20000000000000000000000000000002-2i2−i202-2i2−i20i2−i2i2−i200000i2−i2000
χ332-222022-2-2-2-220-200002222222200-2-2-2-2-2-2-2-2000000000000000000000000000000-22−i2i20-22i2−i20−i2i2−i2i200000i2−i2000
χ342-222022-2-2-2-220-200002222222200-2-2-2-2-2-2-2-2000000000000000000000000000000-22i2−i20-22−i2i20i2−i2i2−i200000−i2i2000
χ354444-4−1−5−1+544−1−5−1+5404-400-4−1−5−1−5−1−5−1−5−1+5−1+5−1+5−1+51+51−5−1−5−1−5−1−5−1−5−1+5−1+5−1+5−1+50-400001+51+51+51+51−51−51−51−50000000000000000000000000000000000000000
χ364444-4−1+5−1−544−1+5−1−5404-400-4−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−51−51+5−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−50-400001−51−51−51−51+51+51+51+50000000000000000000000000000000000000000
χ37444-24−1−5−1+5-24−1−5−1+5-24-2444-2−1−51+521+521+52−1+51−521−521−52−1−5−1+5−1−51+521+521+52−1+51−521−521−52-2-2-2-2−1−5−1+5−1−51+521+521+52−1+51−521−521−52−1−5−1−51+521+521+521+521+521+52−1+5−1+51−521−521−521−521−521−52000000000000000000000000
χ38444-24−1−5−1+5-24−1−5−1+5-2-4-24-4-4-2−1−51+521+521+52−1+51−521−521−52−1−5−1+5−1−51+521+521+52−1+51−521−521−522-2221+51−5−1−51+521+521+52−1+51−521−521−521+51+5−1−52−1−52−1−52−1−52−1−52−1−521−51−5−1+52−1+52−1+52−1+52−1+52−1+52000000000000000000000000
χ39444-24−1+5−1−5-24−1+5−1−5-24-2444-2−1+51−521−521−52−1−51+521+521+52−1+5−1−5−1+51−521−521−52−1−51+521+521+52-2-2-2-2−1+5−1−5−1+51−521−521−52−1−51+521+521+52−1+5−1+51−521−521−521−521−521−52−1−5−1−51+521+521+521+521+521+52000000000000000000000000
χ40444-24−1+5−1−5-24−1+5−1−5-2-4-24-4-4-2−1+51−521−521−52−1−51+521+521+52−1+5−1−5−1+51−521−521−52−1−51+521+521+522-2221−51+5−1+51−521−521−52−1−51+521+521+521−51−5−1+52−1+52−1+52−1+52−1+52−1+521+51+5−1−52−1−52−1−52−1−52−1−52−1−52000000000000000000000000
χ41444-2-444-2444-20-2-40024-2-2-24-2-2-2-4-44-2-2-24-2-2-2020000-4222-42220000000000000000000000000000000000000000
χ42444-2-4−1−5−1+5-24−1−5−1+5-20-2-4002−1−51+521+521+52−1+51−521−521−521+51−5−1−51+521+521+52−1+51−521−521−520200001+5−1−52−1−52−1−521−5−1+52−1+52−1+5200ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ9200−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116000000000000000000000000
χ43444-2-4−1−5−1+5-24−1−5−1+5-20-2-4002−1−51+521+521+52−1+51−521−521−521+51−5−1−51+521+521+52−1+51−521−521−520200001+5−1−52−1−52−1−521−5−1+52−1+52−1+5200−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ9200ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116000000000000000000000000
χ44444-2-4−1+5−1−5-24−1+5−1−5-20-2-4002−1+51−521−521−52−1−51+521+521+521−51+5−1+51−521−521−52−1−51+521+521+520200001−5−1+52−1+52−1+521+5−1−52−1−52−1−5200−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ11600−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92000000000000000000000000
χ45444-2-4−1+5−1−5-24−1+5−1−5-20-2-4002−1+51−521−521−52−1−51+521+521+521−51+5−1+51−521−521−52−1−51+521+521+520200001−5−1+52−1+52−1+521+5−1−52−1−52−1−5200ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ11600ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92000000000000000000000000
χ4644-244−1−5−1+54-2−1−5−1+5-24-2-2-2-241+52−1−51+521+521−52−1+51−521−52−1−5−1+51+52−1−51+521+521−52−1+51−521−524-2-2-2−1−5−1+51+52−1−51+521+521−52−1+51−521−521+521+52−1−5−1−51+521+521+521+521−521−52−1+5−1+51−521−521−521−52000000000000000000000000
χ4744-244−1−5−1+54-2−1−5−1+5-2-4-2-22241+52−1−51+521+521−52−1+51−521−52−1−5−1+51+52−1−51+521+521−52−1+51−521−52-4-2221+51−51+52−1−51+521+521−52−1+51−521−52−1−52−1−521+51+5−1−52−1−52−1−52−1−52−1+52−1+521−51−5−1+52−1+52−1+52−1+52000000000000000000000000
χ4844-244−1+5−1−54-2−1+5−1−5-24-2-2-2-241−52−1+51−521−521+52−1−51+521+52−1+5−1−51−52−1+51−521−521+52−1−51+521+524-2-2-2−1+5−1−51−52−1+51−521−521+52−1−51+521+521−521−52−1+5−1+51−521−521−521−521+521+52−1−5−1−51+521+521+521+52000000000000000000000000
χ4944-244−1+5−1−54-2−1+5−1−5-2-4-2-22241−52−1+51−521−521+52−1−51+521+52−1+5−1−51−52−1+51−521−521+52−1−51+521+52-4-2221−51+51−52−1+51−521−521+52−1−51+521+52−1+52−1+521−51−5−1+52−1+52−1+52−1+52−1−52−1−521+51+5−1−52−1−52−1−52−1−52000000000000000000000000
χ5044-24-4−1−5−1+54-2−1−5−1+5-20-22−2i32i3-41+52−1−51+521+521−52−1+51−521−521+51−51+52−1−51+521+521−52−1+51−521−5202−2i32i300−1−521+5−1−52−1−52−1+521−5−1+52−1+52ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ9200ζ28+ζ52−ζ68−ζ92ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92−ζ28−ζ52+ζ68+ζ92ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ11600ζ4−ζ44+ζ76−ζ116ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116−ζ4+ζ44−ζ76+ζ116000000000000000000000000
χ5144-24-4−1−5−1+54-2−1−5−1+5-20-222i3−2i3-41+52−1−51+521+521−52−1+51−521−521+51−51+52−1−51+521+521−52−1+51−521−52022i3−2i300−1−521+5−1−52−1−52−1+521−5−1+52−1+52−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ9200−ζ28−ζ52+ζ68+ζ92−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92ζ28+ζ52−ζ68−ζ92−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ11600−ζ4+ζ44−ζ76+ζ116−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116ζ4−ζ44+ζ76−ζ116000000000000000000000000
χ5244-24-4−1+5−1−54-2−1+5−1−5-20-22−2i32i3-41−52−1+51−521−521+52−1−51+521+521−51+51−52−1+51−521−521+52−1−51+521+5202−2i32i300−1+521−5−1+52−1+52−1−521+5−1−52−1−52ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ11600ζ4−ζ44+ζ76−ζ116ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116−ζ4+ζ44−ζ76+ζ116ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ9200ζ28+ζ52−ζ68−ζ92ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92−ζ28−ζ52+ζ68+ζ92000000000000000000000000
χ5344-24-4−1+5−1−54-2−1+5−1−5-20-222i3−2i3-41−52−1+51−521−521+52−1−51+521+521−51+51−52−1+51−521−521+52−1−51+521+52022i3−2i300−1+521−5−1+52−1+52−1−521+5−1−52−1−52−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ11600−ζ4+ζ44−ζ76+ζ116−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116ζ4−ζ44+ζ76−ζ116−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ9200−ζ28−ζ52+ζ68+ζ92−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92ζ28+ζ52−ζ68−ζ92000000000000000000000000
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χ878-8-4-40−2−25−2+25442+252−2520-200001+51+5−2ζ28+4ζ52−2ζ68+4ζ924ζ28−2ζ52+4ζ68−2ζ921−51−54ζ4+4ζ44−2ζ76−2ζ116−2ζ4−2ζ44+4ζ76+4ζ11600−1−5−1−52ζ28−4ζ52+2ζ68−4ζ92−4ζ28+2ζ52−4ζ68+2ζ92−1+5−1+5−4ζ4−4ζ44+2ζ76+2ζ1162ζ4+2ζ44−4ζ76−4ζ116000000000000000000000000000000000000000000000000000000
χ888-8-4-40−2−25−2+25442+252−2520-200001+51+54ζ28−2ζ52+4ζ68−2ζ92−2ζ28+4ζ52−2ζ68+4ζ921−51−5−2ζ4−2ζ44+4ζ76+4ζ1164ζ4+4ζ44−2ζ76−2ζ11600−1−5−1−5−4ζ28+2ζ52−4ζ68+2ζ922ζ28−4ζ52+2ζ68−4ζ92−1+5−1+52ζ4+2ζ44−4ζ76−4ζ116−4ζ4−4ζ44+2ζ76+2ζ116000000000000000000000000000000000000000000000000000000
χ898-8-4-40−2+25−2−25442−252+2520-200001−51−54ζ4+4ζ44−2ζ76−2ζ116−2ζ4−2ζ44+4ζ76+4ζ1161+51+54ζ28−2ζ52+4ζ68−2ζ92−2ζ28+4ζ52−2ζ68+4ζ9200−1+5−1+5−4ζ4−4ζ44+2ζ76+2ζ1162ζ4+2ζ44−4ζ76−4ζ116−1−5−1−5−4ζ28+2ζ52−4ζ68+2ζ922ζ28−4ζ52+2ζ68−4ζ92000000000000000000000000000000000000000000000000000000
χ908-8-4-40−2+25−2−25442−252+2520-200001−51−5−2ζ4−2ζ44+4ζ76+4ζ1164ζ4+4ζ44−2ζ76−2ζ1161+51+5−2ζ28+4ζ52−2ζ68+4ζ924ζ28−2ζ52+4ζ68−2ζ9200−1+5−1+52ζ4+2ζ44−4ζ76−4ζ116−4ζ4−4ζ44+2ζ76+2ζ116−1−5−1−52ζ28−4ζ52+2ζ68−4ζ92−4ζ28+2ζ52−4ζ68+2ζ92000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.