Finite Group Databasebeta

← Group #91510

Character table — Group #91510

Order 480.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size11222222244444444444466666688888881212121212121220202020406060
order123455610104121515202020202020303024202020201260606060606021010101010104824241248
χ1111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-111111-1-1
χ4111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111-111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-11-1-1-111-1
χ6111111111-111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1111-1-11
χ7111111111-111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-111111-1-1-11-11
χ8111111111-111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-11111-1111-11-1
χ92222−1−52−1+522−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1+52−1+522−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+52−1−52−1−52−1+52−1+520000000
χ102222−1−52−1+522−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521−521−522−1−52−1+52−1−52−1−52−1+52−1+52-21+521−521+521+521−521−520000000
χ112222−1−52−1+522−1−52−1+52-22−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+5222−1−52−1−52−1+52−1+52-2−1−52−1+521+521+521−521−52-2−1−52−1+521+521+521−521−520000000
χ122222−1−52−1+522−1−52−1+52-22−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+52-2-21+521+521−521−52-2−1−52−1+521+521+521−521−5221+521−52−1−52−1−52−1+52−1+520000000
χ132222−1+52−1−522−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1−52−1−522−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−52−1+52−1+52−1−52−1−520000000
χ142222−1+52−1−522−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521+521+522−1+52−1−52−1+52−1+52−1−52−1−52-21−521+521−521−521+521+520000000
χ152222−1+52−1−522−1+52−1−52-22−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−5222−1+52−1+52−1−52−1−52-2−1+52−1−521−521−521+521+52-2−1+52−1−521−521−521+521+520000000
χ162222−1+52−1−522−1+52−1−52-22−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−52-2-21−521−521+521+52-2−1+52−1−521−521−521+521+5221−521+52−1+52−1+52−1−52−1−520000000
χ17222-2222220-222-2-20000222-2-2-2-2-20-2-2000002200000000000
χ18222-2222220-222-2-2000022-2222220-2-200000-2-200000000000
χ19222-2−1−52−1+522−1−52−1+520-2−1−52−1+521+521−52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116−1−52−1+522-21+521+521−521−5201+521−52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ1160−1−52−1+52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ1160000000
χ20222-2−1−52−1+522−1−52−1+520-2−1−52−1+521+521−52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116−1−52−1+52-22−1−52−1−52−1+52−1+5201+521−52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ11601+521−52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ1160000000
χ21222-2−1−52−1+522−1−52−1+520-2−1−52−1+521+521−52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−1−52−1+522-21+521+521−521−5201+521−52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ1160−1−52−1+52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ1160000000
χ22222-2−1−52−1+522−1−52−1+520-2−1−52−1+521+521−52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−1−52−1+52-22−1−52−1−52−1+52−1+5201+521−52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ11601+521−52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ1160000000
χ23222-2−1+52−1−522−1+52−1−520-2−1+52−1−521−521+52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−1+52−1−522-21−521−521+521+5201−521+52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ920−1+52−1−52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ920000000
χ24222-2−1+52−1−522−1+52−1−520-2−1+52−1−521−521+52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−1+52−1−52-22−1+52−1+52−1−52−1−5201−521+52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ9201−521+52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ920000000
χ25222-2−1+52−1−522−1+52−1−520-2−1+52−1−521−521+52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92−1+52−1−522-21−521−521+521+5201−521+52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ920−1+52−1−52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ920000000
χ26222-2−1+52−1−522−1+52−1−520-2−1+52−1−521−521+52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92−1+52−1−52-22−1+52−1+52−1−52−1−5201−521+52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ9201−521+52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ920000000
χ2722-1222-1222-1-1-1222222-1-1000000-1-1-1-1-1-1-1000000022-1-1-100
χ2822-1222-1222-1-1-1222222-1-1000000-1-1-1-1-1-1-10000000-2-211100
χ2922-1222-122-2-1-1-122-2-2-2-2-1-10000001-1-1111100000002-211-100
χ3022-1222-122-2-1-1-122-2-2-2-2-1-10000001-1-111110000000-22-1-1100
χ3144-24−1−5−1+5-2−1−5−1+54-21+521−52−1−5−1+5−1−5−1−5−1+5−1+51+521−52000000-21+521−521+521+521−521−5200000000000000
χ3244-24−1−5−1+5-2−1−5−1+5-4-21+521−52−1−5−1+51+51+51−51−51+521−5200000021+521−52−1−52−1−52−1+52−1+5200000000000000
χ3344-24−1+5−1−5-2−1+5−1−54-21−521+52−1+5−1−5−1+5−1+5−1−5−1−51−521+52000000-21−521+521−521−521+521+5200000000000000
χ3444-24−1+5−1−5-2−1+5−1−5-4-21−521+52−1+5−1−51−51−51+51+51−521+5200000021−521+52−1+52−1+52−1−52−1−5200000000000000
χ3544-2-444-24402-2-2-4-40000-2-2000000022000000000000000000
χ3644-2-4−1−5−1+5-2−1−5−1+5021+521−521+51−5−2ζ28+2ζ52−2ζ68+2ζ922ζ28−2ζ52+2ζ68−2ζ922ζ4+2ζ44−2ζ76−2ζ116−2ζ4−2ζ44+2ζ76+2ζ1161+521−520000000−1−52−1+52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ11600000000000000
χ3744-2-4−1−5−1+5-2−1−5−1+5021+521−521+51−52ζ28−2ζ52+2ζ68−2ζ92−2ζ28+2ζ52−2ζ68+2ζ92−2ζ4−2ζ44+2ζ76+2ζ1162ζ4+2ζ44−2ζ76−2ζ1161+521−520000000−1−52−1+52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ11600000000000000
χ3844-2-4−1+5−1−5-2−1+5−1−5021−521+521−51+52ζ4+2ζ44−2ζ76−2ζ116−2ζ4−2ζ44+2ζ76+2ζ1162ζ28−2ζ52+2ζ68−2ζ92−2ζ28+2ζ52−2ζ68+2ζ921−521+520000000−1+52−1−52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ9200000000000000
χ3944-2-4−1+5−1−5-2−1+5−1−5021−521+521−51+5−2ζ4−2ζ44+2ζ76+2ζ1162ζ4+2ζ44−2ζ76−2ζ116−2ζ28+2ζ52−2ζ68+2ζ922ζ28−2ζ52+2ζ68−2ζ921−521+520000000−1+52−1−52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ9200000000000000
χ404-44044-4-4-40044000000-4-4000000000000000000000000000
χ414-440−1−5−1+5-41+51−500−1−5−1+50000001+51−500−2ζ22+2ζ38−2ζ62+2ζ1182ζ22−2ζ38+2ζ62−2ζ1182ζ14−2ζ46−2ζ86+2ζ94−2ζ14+2ζ46+2ζ86−2ζ94000000000000000000000
χ424-440−1−5−1+5-41+51−500−1−5−1+50000001+51−5002ζ22−2ζ38+2ζ62−2ζ118−2ζ22+2ζ38−2ζ62+2ζ118−2ζ14+2ζ46+2ζ86−2ζ942ζ14−2ζ46−2ζ86+2ζ94000000000000000000000
χ434-440−1+5−1−5-41−51+500−1+5−1−50000001−51+5002ζ14−2ζ46−2ζ86+2ζ94−2ζ14+2ζ46+2ζ86−2ζ942ζ22−2ζ38+2ζ62−2ζ118−2ζ22+2ζ38−2ζ62+2ζ118000000000000000000000
χ444-440−1+5−1−5-41−51+500−1+5−1−50000001−51+500−2ζ14+2ζ46+2ζ86−2ζ942ζ14−2ζ46−2ζ86+2ζ94−2ζ22+2ζ38−2ζ62+2ζ1182ζ22−2ζ38+2ζ62−2ζ118000000000000000000000
χ454-4-20442-4-400-2-2000000220000000000000000000000−i6i6000
χ464-4-20442-4-400-2-2000000220000000000000000000000i6−i6000
χ478-8-40−2−25−2+2542+252−25001+51−5000000−1−5−1+5000000000000000000000000000
χ488-8-40−2+25−2−2542−252+25001−51+5000000−1+5−1−5000000000000000000000000000

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