Finite Group Databasebeta

← Group #65239

Character table — Group #65239

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222222222224444444444444444444444444444101010101010101020202020
order1222222222225510101010101010101010101010104444101010101010101020202020202020202020202020202020444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ1011-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ1111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ1211-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−i
χ1311-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ1411-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ1511-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−i
χ1611-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−ii
χ17222222222222−1+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+52−1−52−1−52000000000000
χ18222222222222−1+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+52−1−52−1−52-2-2-2-2−1+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+52000000000000
χ19222222222222−1−52−1+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+52000000000000
χ20222222222222−1−52−1+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+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000
χ2122222222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−5222-2-21−521−521+521+521−521−521+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+52000000000000
χ2222222222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52-2-2221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ2322222222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+5222-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000
χ2422222222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52-2-2221+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ252222-2-2-2-22-22-2222222-2-222-2-2-2-2-2-200002-22-22-22-20000000000000000000000000000
χ262222-2-2-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+521−521−521+521+520000−1+521−52−1−521+52−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ272222-2-2-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+521−521−521+521+520000−1+521−52−1−521+52−1+521−52−1−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ282222-2-2-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−521+521+521−521−520000−1−521+52−1+521−52−1−521+52−1+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ292222-2-2-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−521+521+521−521−520000−1−521+52−1+521−52−1−521+52−1+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ302222-2-2-2-2-22-22222222-2-222-2-2-2-2-2-20000-22-22-22-220000000000000000000000000000
χ312222-2-2-2-2-22-22−1+52−1−52−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+521−521−521+521+5200001−52−1+521+52−1−521−52−1+521+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ322222-2-2-2-2-22-22−1+52−1−52−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+521−521−521+521+5200001−52−1+521+52−1−521−52−1+521+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ332222-2-2-2-2-22-22−1−52−1+52−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−521+521+521−521−5200001+52−1−521−52−1+521+52−1−521−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ342222-2-2-2-2-22-22−1−52−1+52−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−521+521+521−521−5200001+52−1−521−52−1+521+52−1−521−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ3522-2-222-2-222-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−522-22-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ3622-2-222-2-222-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-22-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000
χ3722-2-222-2-222-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+522-22-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000
χ3822-2-222-2-222-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-22-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000
χ3922-2-222-2-2-2-222−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−522-2-221−521−521+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+52−1+52−1+52−1−52−1−52000000000000
χ4022-2-222-2-2-2-222−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ4122-2-222-2-2-2-222−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+522-2-221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000
χ4222-2-222-2-2-2-222−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-222-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000
χ4322-2-2-2-2222-2-222222-2-222-2-222-2-2-2-200002-22-2-22-220000000000000000000000000000
χ4422-2-2-2-2222-2-22−1+52−1−52−1+52−1−521−521−52−1+52−1+521+521+52−1−52−1−521−521−521+521+520000−1+521−52−1−521+521−52−1+521+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ4522-2-2-2-2222-2-22−1+52−1−52−1+52−1−521−521−52−1+52−1+521+521+52−1−52−1−521−521−521+521+520000−1+521−52−1−521+521−52−1+521+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ4622-2-2-2-2222-2-22−1−52−1+52−1−52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+521−521−520000−1−521+52−1+521−521+52−1−521−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ4722-2-2-2-2222-2-22−1−52−1+52−1−52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+521−521−520000−1−521+52−1+521−521+52−1−521−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ4822-2-2-2-222-222-22222-2-222-2-222-2-2-2-20000-22-222-22-20000000000000000000000000000
χ4922-2-2-2-222-222-2−1+52−1−52−1+52−1−521−521−52−1+52−1+521+521+52−1−52−1−521−521−521+521+5200001−52−1+521+52−1−52−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ5022-2-2-2-222-222-2−1+52−1−52−1+52−1−521−521−52−1+52−1+521+521+52−1−52−1−521−521−521+521+5200001−52−1+521+52−1−52−1+521−52−1−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ5122-2-2-2-222-222-2−1−52−1+52−1−52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+521−521−5200001+52−1−521−52−1+52−1−521+52−1+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ5222-2-2-2-222-222-2−1−52−1+52−1−52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+521−521−5200001+52−1−521−52−1+52−1−521+52−1+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ532-22-22-22-2000022-2-22-22-22-22-22-22-2000000000000000000000000000000002i−2i2i−2i0000
χ542-22-22-22-2000022-2-22-22-22-22-22-22-200000000000000000000000000000000−2i2i−2i2i0000
χ552-22-2-22-22000022-2-22-2-222-2-22-22-2200000000000000000000000000002-22-200000000
χ562-22-2-22-22000022-2-22-2-222-2-22-22-220000000000000000000000000000-22-2200000000
χ572-2-222-2-22000022-2-2-22-22-22-222-22-2000000000000000000000000000000002-2-220000
χ582-2-222-2-22000022-2-2-22-22-22-222-22-200000000000000000000000000000000-222-20000
χ592-2-22-222-2000022-2-2-222-2-222-2-22-2200000000000000000000000000002i−2i−2i2i00000000
χ602-2-22-222-2000022-2-2-222-2-222-2-22-220000000000000000000000000000−2i2i2i−2i00000000
χ614-44-44-44-40000−1+5−1−51−51+5−1+51−5−1+51−5−1−51+5−1−51+5−1+51−5−1−51+50000000000000000000000000000000000000000
χ624-44-44-44-40000−1−5−1+51+51−5−1−51+5−1−51+5−1+51−5−1+51−5−1−51+5−1+51−50000000000000000000000000000000000000000
χ634-44-4-44-440000−1+5−1−51−51+5−1+51−51−5−1+5−1−51+51+5−1−51−5−1+51+5−1−50000000000000000000000000000000000000000
χ644-44-4-44-440000−1−5−1+51+51−5−1−51+51+5−1−5−1+51−51−5−1+51+5−1−51−5−1+50000000000000000000000000000000000000000
χ654-4-444-4-440000−1+5−1−51−51+51−5−1+51−5−1+51+5−1−51+5−1−5−1+51−5−1−51+50000000000000000000000000000000000000000
χ664-4-444-4-440000−1−5−1+51+51−51+5−1−51+5−1−51−5−1+51−5−1+5−1−51+5−1+51−50000000000000000000000000000000000000000
χ674-4-44-444-40000−1+5−1−51−51+51−5−1+5−1+51−51+5−1−5−1−51+51−5−1+51+5−1−50000000000000000000000000000000000000000
χ684-4-44-444-40000−1−5−1+51+51−51+5−1−5−1−51+51−5−1+5−1+51−51+5−1−51−5−1+50000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.