Finite Group Databasebeta

← Group #66085

Character table — Group #66085

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222222222222222222222224444444444444444444444444442020202020202020
order1222244445588101020202020404040404040404088810101010101020202020202040404040404040404040404022224444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1
χ411111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ5111-1-11-1-111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1
χ6111-1-11-1-111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11
χ7111-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-11-1-1-11
χ8111-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1111-1
χ911-11-1-11-11111111111111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-1-11-11
χ1011-11-1-11-11111111111111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-111-11-1
χ1111-11-1-11-1111-1-1111111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111-1-11111-1-1-1-111111-111-1-11-1
χ1211-11-1-11-1111-1-1111111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111-1-11111-1-1-1-11111-11-1-111-11
χ1311-1-11-1-111111111111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1111-1-1
χ1411-1-11-1-111111111111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-111-1-1-111
χ1511-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111111111-1-1-1-11-1-1-11-111
χ1611-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1111-11-1-1
χ17222222222−1+52−1−5222−1+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+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ18222222222−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-2-2-2−1+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+521−521−521+521+521−521−521+521+5200000000
χ19222222222−1−52−1+5222−1−52−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000
χ20222222222−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−5200000000
χ212222-2-2-22-2220022-2-2-2-2000000000002222-2-2-2-2-2-22200000000000000000000
χ222222-2-2-22-2−1+52−1−5200−1+52−1−521−521−521+521+52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14000−1+52−1−52−1+52−1−521−521+521−521+521−521+52−1+52−1−52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000
χ232222-2-2-22-2−1+52−1−5200−1+52−1−521−521−521+521+52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14000−1+52−1−52−1+52−1−521−521+521−521+521−521+52−1+52−1−52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000
χ242222-2-2-22-2−1−52−1+5200−1−52−1+521+521+521−521−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38000−1−52−1+52−1−52−1+521+521−521+521−521+521−52−1−52−1+52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000
χ252222-2-2-22-2−1−52−1+5200−1−52−1+521+521+521−521−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38000−1−52−1+52−1−52−1+521+521−521+521−521+521−52−1−52−1+52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000
χ26222-22-22-2-2220022-2-2-2-20000000000022-2-222-2-222-2-200000000000000000000
χ27222-22-22-2-2−1+52−1−5200−1+52−1−521−521−521+521+52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14000−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000
χ28222-22-22-2-2−1+52−1−5200−1+52−1−521−521−521+521+52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14000−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000
χ29222-22-22-2-2−1−52−1+5200−1−52−1+521+521+521−521−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38000−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+521+521−52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000
χ30222-22-22-2-2−1−52−1+5200−1−52−1+521+521+521−521−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38000−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+521+521−52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000
χ31222-2-22-2-22−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-2−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000
χ32222-2-22-2-22−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-222−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ33222-2-22-2-22−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-2-2−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000
χ34222-2-22-2-22−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-222−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000
χ3522-2222-2-2-2220022-2-2-2-200000000000-2-2222222-2-2-2-200000000000000000000
χ3622-2222-2-2-2−1+52−1−5200−1+52−1−521−521−521+521+52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ140001−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000
χ3722-2222-2-2-2−1+52−1−5200−1+52−1−521−521−521+521+52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ140001−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000
χ3822-2222-2-2-2−1−52−1+5200−1−52−1+521+521+521−521−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ380001+521−52−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000
χ3922-2222-2-2-2−1−52−1+5200−1−52−1+521+521+521−521−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ380001+521−52−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000
χ4022-22-2-22-22−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-22-21−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000
χ4122-22-2-22-22−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+522-221−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000
χ4222-22-2-22-22−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-22-21+521−52−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000
χ4322-22-2-22-22−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−522-221+521−52−1−52−1+521+521−521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200000000
χ4422-2-22-2-222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-221−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000
χ4522-2-22-2-222−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5222-21−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000
χ4622-2-22-2-222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-221+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000
χ4722-2-22-2-222−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5222-21+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000000
χ4822-2-2-2222-2220022-2-2-2-200000000000-2-2-2-2-2-222222200000000000000000000
χ4922-2-2-2222-2−1+52−1−5200−1+52−1−521−521−521+521+52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ140001−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000
χ5022-2-2-2222-2−1+52−1−5200−1+52−1−521−521−521+521+52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ140001−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000
χ5122-2-2-2222-2−1−52−1+5200−1−52−1+521+521+521−521−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ380001+521−521+521−521+521−52−1−52−1+52−1−52−1+52−1−52−1+52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000
χ5222-2-2-2222-2−1−52−1+5200−1−52−1+521+521+521−521−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ380001+521−521+521−521+521−52−1−52−1+52−1−52−1+52−1−52−1+52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000
χ534-40000000442i2−2i2-4-400002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000
χ544-4000000044−2i22i2-4-40000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000
χ554-40000000−1+5−1−52i2−2i21−51+5−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ142ζ7+2ζ13−2ζ7−2ζ132ζ23+2ζ37−2ζ23−2ζ372ζ21+2ζ39−2ζ21−2ζ392ζ29+2ζ31−2ζ29−2ζ3100000000000000000000000000000000000
χ564-40000000−1+5−1−52i2−2i21−51+52ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ23+2ζ37−2ζ23−2ζ372ζ7+2ζ13−2ζ7−2ζ132ζ29+2ζ31−2ζ29−2ζ312ζ21+2ζ39−2ζ21−2ζ3900000000000000000000000000000000000
χ574-40000000−1+5−1−5−2i22i21−51+5−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ7−2ζ132ζ7+2ζ13−2ζ23−2ζ372ζ23+2ζ37−2ζ21−2ζ392ζ21+2ζ39−2ζ29−2ζ312ζ29+2ζ3100000000000000000000000000000000000
χ584-40000000−1+5−1−5−2i22i21−51+52ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14−2ζ23−2ζ372ζ23+2ζ37−2ζ7−2ζ132ζ7+2ζ13−2ζ29−2ζ312ζ29+2ζ31−2ζ21−2ζ392ζ21+2ζ3900000000000000000000000000000000000
χ594-40000000−1−5−1+52i2−2i21+51−52ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ21+2ζ39−2ζ21−2ζ392ζ29+2ζ31−2ζ29−2ζ312ζ23+2ζ37−2ζ23−2ζ372ζ7+2ζ13−2ζ7−2ζ1300000000000000000000000000000000000
χ604-40000000−1−5−1+52i2−2i21+51−5−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ382ζ29+2ζ31−2ζ29−2ζ312ζ21+2ζ39−2ζ21−2ζ392ζ7+2ζ13−2ζ7−2ζ132ζ23+2ζ37−2ζ23−2ζ3700000000000000000000000000000000000
χ614-40000000−1−5−1+5−2i22i21+51−52ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38−2ζ21−2ζ392ζ21+2ζ39−2ζ29−2ζ312ζ29+2ζ31−2ζ23−2ζ372ζ23+2ζ37−2ζ7−2ζ132ζ7+2ζ1300000000000000000000000000000000000
χ624-40000000−1−5−1+5−2i22i21+51−5−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ29−2ζ312ζ29+2ζ31−2ζ21−2ζ392ζ21+2ζ39−2ζ7−2ζ132ζ7+2ζ13−2ζ23−2ζ372ζ23+2ζ3700000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.