Finite Group Databasebeta

← Group #277322

Character table — Group #277322

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ172222222222-2-22-22-200000000-22222-222220000-2-2-2-2000000000000-2-222-2-200000000000000000000
χ182222222222-2-22-22-200000000-22222-2-2-2-2-200002222000000000000-2-2-2-22200000000000000000000
χ192222222222-2-22-22-200000000-2-2-2-2-2-222220000-2-2-2-200000000000022-2-22200000000000000000000
χ202222222222-2-22-22-200000000-2-2-2-2-2-2-2-2-2-2000022220000000000002222-2-200000000000000000000
χ2122222222-2-222-22-2222222222-20000-20000-2-2-2-2000000000000222200000000000000-2-20000000000
χ2222222222-2-222-22-2222222222-20000-20000-2-2-2-2000000000000-2-2-2-200000000000000220000000000
χ2322222222-2-222-22-22-2-2-2-2-2-2-2-2-20000-20000222200000000000022-2-200000000000000-220000000000
χ2422222222-2-222-22-22-2-2-2-2-2-2-2-2-20000-200002222000000000000-2-222000000000000002-20000000000
χ25222-22-2-2-22-20020-202222−2−2−2−2022-2-2022-2-222−2−200002222−2−2−2−20000002-20022−2−222−2−2000000000000
χ26222-22-2-2-22-20020-202222−2−2−2−2022-2-20-2-22222−2−20000−2−2−2−22222000000-220022−2−2−2−222000000000000
χ27222-22-2-2-22-20020-202222−2−2−2−20-2-222022-2-222−2−200002222−2−2−2−2000000-2200−2−222−2−222000000000000
χ28222-22-2-2-22-20020-202222−2−2−2−20-2-2220-2-22222−2−20000−2−2−2−222220000002-200−2−22222−2−2000000000000
χ29222-22-2-2-22-20020-20−2−2−2−22222022-2-2022-2-2−2−2220000−2−2−2−222220000002-200−2−222−2−222000000000000
χ30222-22-2-2-22-20020-20−2−2−2−22222022-2-20-2-222−2−22200002222−2−2−2−2000000-2200−2−22222−2−2000000000000
χ31222-22-2-2-22-20020-20−2−2−2−222220-2-222022-2-2−2−2220000−2−2−2−22222000000-220022−2−222−2−2000000000000
χ32222-22-2-2-22-20020-20−2−2−2−222220-2-2220-2-222−2−22200002222−2−2−2−20000002-20022−2−2−2−222000000000000
χ3322-2-2-2-222002-2020-222-2-222-2-20000002−22−2000022−2−222−2−222−2−22i−2i2i−2i00000000000000000000i2−i2i2−i200
χ3422-2-2-2-222002-2020-222-2-222-2-20000002−22−2000022−2−222−2−222−2−2−2i2i−2i2i00000000000000000000−i2i2−i2i200
χ3522-2-2-2-222002-2020-222-2-222-2-2000000−22−220000−2−222−2−222−2−2222i−2i2i−2i00000000000000000000−i2i2−i2i200
χ3622-2-2-2-222002-2020-222-2-222-2-2000000−22−220000−2−222−2−222−2−222−2i2i−2i2i00000000000000000000i2−i2i2−i200
χ3722-2-2-2-222002-2020-2-2-222-2-2220000002−22−2000022−2−2−2−222−2−2222i−2i−2i2i00000000000000000000i2−i2−i2i200
χ3822-2-2-2-222002-2020-2-2-222-2-2220000002−22−2000022−2−2−2−222−2−222−2i2i2i−2i00000000000000000000−i2i2i2−i200
χ3922-2-2-2-222002-2020-2-2-222-2-222000000−22−220000−2−22222−2−222−2−22i−2i−2i2i00000000000000000000−i2i2i2−i200
χ4022-2-2-2-222002-2020-2-2-222-2-222000000−22−220000−2−22222−2−222−2−2−2i2i2i−2i00000000000000000000i2−i2−i2i200
χ412-2-222-2-22-220020-202−22−22−22−202-22-2000002−22−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000002i−2i2−22−2i2−i2i2−i2000000000000
χ422-2-222-2-22-220020-202−22−22−22−202-22-2000002−22−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000−2i2i2−22−2−i2i2−i2i2000000000000
χ432-2-222-2-22-220020-202−22−22−22−20-22-22000002−22−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000−2i2i−22−22−i2i2−i2i2000000000000
χ442-2-222-2-22-220020-202−22−22−22−20-22-22000002−22−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000002i−2i−22−22i2−i2i2−i2000000000000
χ452-2-222-2-22-220020-20−22−22−22−2202-22-200000−22−222i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000002i−2i−22−22−i2i2−i2i2000000000000
χ462-2-222-2-22-220020-20−22−22−22−2202-22-200000−22−22−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000−2i2i−22−22i2−i2i2−i2000000000000
χ472-2-222-2-22-220020-20−22−22−22−220-22-2200000−22−222i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000−2i2i2−22−2i2−i2i2−i2000000000000
χ482-2-222-2-22-220020-20−22−22−22−220-22-2200000−22−22−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000002i−2i2−22−2−i2i2−i2i2000000000000
χ492-2-2-2222-222-2-2-22-222-22-2-22-2220000-20000-222-2000000000000000000000000000000002i−2i2i−2i000000
χ502-2-2-2222-222-2-2-22-222-22-2-22-2220000-20000-222-200000000000000000000000000000000−2i2i−2i2i000000
χ512-2-2-2222-222-2-2-22-22-22-222-22-220000-200002-2-22000000000000000000000000000000002i−2i−2i2i000000
χ522-2-2-2222-222-2-2-22-22-22-222-22-220000-200002-2-2200000000000000000000000000000000−2i2i2i−2i000000
χ532-2-2-2222-2-2-2222-22-20000000022-2-22-20000000000002i−2i2i−2i−2i2i−2i2i00002-2000000002i−2i−2i2i000000000000
χ542-2-2-2222-2-2-2222-22-20000000022-2-22-2000000000000−2i2i−2i2i2i−2i2i−2i00002-200000000−2i2i2i−2i000000000000
χ552-2-2-2222-2-2-2222-22-2000000002-222-2-20000000000002i−2i2i−2i−2i2i−2i2i0000-2200000000−2i2i2i−2i000000000000
χ562-2-2-2222-2-2-2222-22-2000000002-222-2-2000000000000−2i2i−2i2i2i−2i2i−2i0000-22000000002i−2i−2i2i000000000000
χ572-2-2-2222-2-2-2-2-222222-22-2-22-22-22-2-22200002-2-220000000000000000-2200002-2-220000000000000000
χ582-2-2-2222-2-2-2-2-222222-22-2-22-22-2-222-2200002-2-2200000000000000002-20000-222-20000000000000000
χ592-2-2-2222-2-2-2-2-22222-22-222-22-2-22-2-2220000-222-20000000000000000-220000-222-20000000000000000
χ602-2-2-2222-2-2-2-2-22222-22-222-22-2-2-222-220000-222-200000000000000002-200002-2-220000000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4400-404022222222−22−22−22−220000000000−22−222222000000000000000000000000000000000000000000
χ63444-44-4-4-4-4400-4040−22−22−22−222222222200000000002222−22−22000000000000000000000000000000000000000000
χ6444-44-44-4-4000000002222−22−22−22−22222200000022−22−22220000000022-2-2-2-222000000000000000000000000000000
χ6544-44-44-4-4000000002222−22−22−22−222222000000−222222−2200000000-2-22222-2-2000000000000000000000000000000
χ6644-44-44-4-400000000−22−2222222222−22−2200000022−22−222200000000-2-22222-2-2000000000000000000000000000000
χ6744-44-44-4-400000000−22−2222222222−22−22000000−222222−220000000022-2-2-2-222000000000000000000000000000000
χ6844-4-4-4-44400-440-4040000000000000022−2222−220000−22−22222200000000000000000000000000000000000000
χ6944-4-4-4-44400-440-40400000000000000−2222−222200002222−22−2200000000000000000000000000000000000000
χ704-444-4-44-4004-40-404000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ714-444-4-44-4004-40-40400000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ724-444-4-44-400-44040-44-4-44-444-400000000000000000000000000000000000000000000000000000000
χ734-444-4-44-400-44040-4-444-44-4-4400000000000000000000000000000000000000000000000000000000
χ744-44-4-44-440000000022−22−222222−22−2222000000000000002i2−2i2−2i22i22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ754-44-4-44-440000000022−22−222222−22−222200000000000000−2i22i22i2−2i2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ764-44-4-44-4400000000−222222−22−222222−22000000000000002i2−2i2−2i22i2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ774-44-4-44-4400000000−222222−22−222222−2200000000000000−2i22i22i2−2i22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ784-4-444-4-444-400-404022−2222−2222−2222−220000000000−2222−2222000000000000000000000000000000000000000000
χ794-4-444-4-444-400-4040−2222−2222−2222−2222000000000022−2222−22000000000000000000000000000000000000000000
χ804-4-4-4444-44444-4-4-4-400000000-40000400000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).