Finite Group Databasebeta

← Group #307378

Character table — Group #307378

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-11-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-11-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1111111-1-11-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1111-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-11-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-111-1-1-1111-1-1-11
χ17222222222-222-2-22-2000000002222-2-200002222-2-2-2-200000000220000-2-2-2-200000000000000000000
χ18222222222-222-2-22-2000000002222-2-20000-2-2-2-2222200000000-2-20000-2-22200000000000000000000
χ19222222222-222-2-22-200000000-2-2-2-2-2-200002222-2-2-2-200000000-2-20000222200000000000000000000
χ20222222222-222-2-22-200000000-2-2-2-2-2-20000-2-2-2-222220000000022000022-2-200000000000000000000
χ2122222222-22-2-222-22222222220000-2-2-2-2-2-200000000000000000022220000000000000000-2-2000000
χ2222222222-22-2-222-22222222220000-2-2-2-2-2-2000000000000000000-2-2-2-2000000000000000022000000
χ2322222222-22-2-222-22-2-2-2-2-2-2-2-20000-2-2222200000000000000000022-2-20000000000000000-22000000
χ2422222222-22-2-222-22-2-2-2-2-2-2-2-20000-2-22222000000000000000000-2-22200000000000000002-2000000
χ25222-2-22-2-202002-20-22222-2-2-2-2000000000022−2−222−2−22222−2−2−2−2002-22-20000000000000000002−22−200
χ26222-2-22-2-202002-20-22222-2-2-2-2000000000022−2−222−2−22222−2−2−2−200-22-22000000000000000000−22−2200
χ27222-2-22-2-202002-20-22222-2-2-2-20000000000−2−222−2−222−2−2−2−22222002-22-2000000000000000000−22−2200
χ28222-2-22-2-202002-20-22222-2-2-2-20000000000−2−222−2−222−2−2−2−2222200-22-220000000000000000002−22−200
χ29222-2-22-2-202002-20-2-2-2-2-22222000000000022−2−222−2−2−2−2−2−22222002-2-220000000000000000002−2−2200
χ30222-2-22-2-202002-20-2-2-2-2-22222000000000022−2−222−2−2−2−2−2−2222200-222-2000000000000000000−222−200
χ31222-2-22-2-202002-20-2-2-2-2-222220000000000−2−222−2−2222222−2−2−2−2002-2-22000000000000000000−222−200
χ32222-2-22-2-202002-20-2-2-2-2-222220000000000−2−222−2−2222222−2−2−2−200-222-20000000000000000002−2−2200
χ3322-222-2-2-2202-200-2022−2−222−2−222-2-20022−2−22-22-2000022−2−222−2−22-20000000022−2−222−2−2000000000000
χ3422-222-2-2-2202-200-2022−2−222−2−222-2-20022−2−2-22-220000−2−222−2−222-220000000022−2−2−2−222000000000000
χ3522-222-2-2-2202-200-2022−2−222−2−2-2-2220022−2−22-22-2000022−2−222−2−2-2200000000−2−222−2−222000000000000
χ3622-222-2-2-2202-200-2022−2−222−2−2-2-2220022−2−2-22-220000−2−222−2−2222-200000000−2−22222−2−2000000000000
χ3722-222-2-2-2202-200-20−2−222−2−22222-2-200−2−2222-22-20000−2−222−2−2222-200000000−2−222−2−222000000000000
χ3822-222-2-2-2202-200-20−2−222−2−22222-2-200−2−222-22-22000022−2−222−2−2-2200000000−2−22222−2−2000000000000
χ3922-222-2-2-2202-200-20−2−222−2−222-2-22200−2−2222-22-20000−2−222−2−222-220000000022−2−222−2−2000000000000
χ4022-222-2-2-2202-200-20−2−222−2−222-2-22200−2−222-22-22000022−2−222−2−22-20000000022−2−2−2−222000000000000
χ412-222-2-22-2-202-200202−22−22−22−22i−2i2i−2i002−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000002-2i2−i2i2−i22−22−2000000000000
χ422-222-2-22-2-202-200202−22−22−22−22i−2i2i−2i002−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000-22i2−i2i2−i2−22−22000000000000
χ432-222-2-22-2-202-200202−22−22−22−2−2i2i−2i2i002−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000-22−i2i2−i2i2−22−22000000000000
χ442-222-2-22-2-202-200202−22−22−22−2−2i2i−2i2i002−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000002-2−i2i2−i2i22−22−2000000000000
χ452-222-2-22-2-202-20020−22−22−22−222i−2i2i−2i00−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000002-2−i2i2−i2i2−22−22000000000000
χ462-222-2-22-2-202-20020−22−22−22−222i−2i2i−2i00−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000-22−i2i2−i2i22−22−2000000000000
χ472-222-2-22-2-202-20020−22−22−22−22−2i2i−2i2i00−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000-22i2−i2i2−i22−22−2000000000000
χ482-222-2-22-2-202-20020−22−22−22−22−2i2i−2i2i00−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000002-2i2−i2i2−i2−22−22000000000000
χ492-2-22-22-222-2-2-2222-22-2-222-2-2200002-2-222-200000000000000000000000000000000002i−2i2i−2i00000000
χ502-2-22-22-222-2-2-2222-22-2-222-2-2200002-2-222-20000000000000000000000000000000000−2i2i−2i2i00000000
χ512-2-22-22-222-2-2-2222-2-222-2-222-200002-22-2-2200000000000000000000000000000000002i−2i−2i2i00000000
χ522-2-22-22-222-2-2-2222-2-222-2-222-200002-22-2-220000000000000000000000000000000000−2i2i2i−2i00000000
χ532-2-22-22-22-2222-2-2-22000000002i−2i−2i2i2-20000000000002i−2i−2i2i2i−2i−2i2i0000002i−2i0000002-2-22000000000000
χ542-2-22-22-22-2222-2-2-22000000002i−2i−2i2i2-2000000000000−2i2i2i−2i−2i2i2i−2i0000002i−2i000000-222-2000000000000
χ552-2-22-22-22-2222-2-2-2200000000−2i2i2i−2i2-20000000000002i−2i−2i2i2i−2i−2i2i000000−2i2i000000-222-2000000000000
χ562-2-22-22-22-2222-2-2-2200000000−2i2i2i−2i2-2000000000000−2i2i2i−2i−2i2i2i−2i000000−2i2i0000002-2-22000000000000
χ572-2-22-22-22-2-22222-2-22-2-222-2-222i−2i−2i2i-222-2-220000000000000000000000−2i2i002i−2i−2i2i0000000000000000
χ582-2-22-22-22-2-22222-2-22-2-222-2-22−2i2i2i−2i-222-2-2200000000000000000000002i−2i00−2i2i2i−2i0000000000000000
χ592-2-22-22-22-2-22222-2-2-222-2-222-22i−2i−2i2i-22-222-20000000000000000000000−2i2i00−2i2i2i−2i0000000000000000
χ602-2-22-22-22-2-22222-2-2-222-2-222-2−2i2i2i−2i-22-222-200000000000000000000002i−2i002i−2i−2i2i0000000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-44-4-40-400-44040000000000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ63444-4-44-4-40-400-4404000000000000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ6444-444-4-4-4-40-4400402222−22−222222−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ6544-444-4-4-4-40-440040−22−222222−22−2222220000002222−22−220000000000000000000000000000000000000000000000
χ6644-4-4-4-444000000002222−22−22−22−222222000000000022−22−2222000022-2-2-2-222000000000000000000000000000000
χ6744-4-4-4-444000000002222−22−22−22−2222220000000000−222222−220000-2-22222-2-2000000000000000000000000000000
χ6844-4-4-4-44400000000−22−2222222222−22−22000000000022−22−22220000-2-22222-2-2000000000000000000000000000000
χ6944-4-4-4-44400000000−22−2222222222−22−220000000000−222222−22000022-2-2-2-222000000000000000000000000000000
χ704-444-4-44-440-4400-4022−2222−2222−2222−22000000−2222−22220000000000000000000000000000000000000000000000
χ714-444-4-44-440-4400-40−2222−2222−2222−222200000022−2222−220000000000000000000000000000000000000000000000
χ724-44-44-4-440000000022−2222−22−2222−2222000000000000002i2−2i2−2i22i22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-44-44-4-440000000022−2222−22−2222−222200000000000000−2i22i22i2−2i2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ744-44-44-4-4400000000−2222−222222−2222−22000000000000002i2−2i2−2i22i2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ754-44-44-4-4400000000−2222−222222−2222−2200000000000000−2i22i22i2−2i22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ764-4-44-44-4444-4-4-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ774-4-4-4444-40400-440-4000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ784-4-4-4444-40400-440-400000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ794-4-4-4444-40-4004-4044-4-44-444-400000000000000000000000000000000000000000000000000000000
χ804-4-4-4444-40-4004-404-444-44-4-4400000000000000000000000000000000000000000000000000000000

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