Finite Group Databasebeta

← Group #307376

Character table — Group #307376

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
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ17222222222-222-2-22-2222222220000-2-2-2-2-2-20000000000000000002222000000000000-2-20000000000
χ18222222222-222-2-22-2222222220000-2-2-2-2-2-2000000000000000000-2-2-2-2000000000000220000000000
χ19222222222-222-2-22-2-2-2-2-2-2-2-2-20000-2-2222200000000000000000022-2-2000000000000-220000000000
χ20222222222-222-2-22-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000-2-2220000000000002-20000000000
χ2122222222-22-2-222-22000000002222-2-200002222-2-2-2-200000000220000-2-2-2-200000000000000000000
χ2222222222-22-2-222-22000000002222-2-20000-2-2-2-2222200000000-2-20000-2-22200000000000000000000
χ2322222222-22-2-222-2200000000-2-2-2-2-2-200002222-2-2-2-200000000-2-20000222200000000000000000000
χ2422222222-22-2-222-2200000000-2-2-2-2-2-20000-2-2-2-222220000000022000022-2-200000000000000000000
χ25222-22-2-2-2202-200-202222-2-2-2-2000000000022−2−222−2−22222−2−2−2−2002-22-20000000000000000002−22−200
χ26222-22-2-2-2202-200-202222-2-2-2-2000000000022−2−222−2−22222−2−2−2−200-22-22000000000000000000−22−2200
χ27222-22-2-2-2202-200-202222-2-2-2-20000000000−2−222−2−222−2−2−2−22222002-22-2000000000000000000−22−2200
χ28222-22-2-2-2202-200-202222-2-2-2-20000000000−2−222−2−222−2−2−2−2222200-22-220000000000000000002−22−200
χ29222-22-2-2-2202-200-20-2-2-2-22222000000000022−2−222−2−2−2−2−2−22222002-2-220000000000000000002−2−2200
χ30222-22-2-2-2202-200-20-2-2-2-22222000000000022−2−222−2−2−2−2−2−2222200-222-2000000000000000000−222−200
χ31222-22-2-2-2202-200-20-2-2-2-222220000000000−2−222−2−2222222−2−2−2−2002-2-22000000000000000000−222−200
χ32222-22-2-2-2202-200-20-2-2-2-222220000000000−2−222−2−2222222−2−2−2−200-222-20000000000000000002−2−2200
χ3322-22-2-22-20-2002-20222−2−222−2−222-2-20022−2−200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000002i−2i22−2−2i2i2−i2−i2000000000000
χ3422-22-2-22-20-2002-20222−2−222−2−222-2-20022−2−20000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200000000−2i2i22−2−2−i2−i2i2i2000000000000
χ3522-22-2-22-20-2002-20222−2−222−2−2-2-2220022−2−200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i200000000−2i2i−2−222−i2−i2i2i2000000000000
χ3622-22-2-22-20-2002-20222−2−222−2−2-2-2220022−2−20000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000002i−2i−2−222i2i2−i2−i2000000000000
χ3722-22-2-22-20-2002-202−2−222−2−22222-2-200−2−22200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2000000002i−2i−2−222−i2−i2i2i2000000000000
χ3822-22-2-22-20-2002-202−2−222−2−22222-2-200−2−2220000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200000000−2i2i−2−222i2i2−i2−i2000000000000
χ3922-22-2-22-20-2002-202−2−222−2−222-2-22200−2−22200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i200000000−2i2i22−2−2i2i2−i2−i2000000000000
χ4022-22-2-22-20-2002-202−2−222−2−222-2-22200−2−2220000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000000002i−2i22−2−2−i2−i2i2i2000000000000
χ412-22-2-2-22202002-20-22−22−22−22−22i−2i2i−2i002−22−22-22-200002−22−22−22−22i−2i00000000i2−i2i2−i2i2−i2i2−i2000000000000
χ422-22-2-2-22202002-20-22−22−22−22−22i−2i2i−2i002−22−2-22-220000−22−22−22−22−2i2i00000000i2−i2i2−i2−i2i2−i2i2000000000000
χ432-22-2-2-22202002-20-22−22−22−22−2−2i2i−2i2i002−22−22-22-200002−22−22−22−2−2i2i00000000−i2i2−i2i2−i2i2−i2i2000000000000
χ442-22-2-2-22202002-20-22−22−22−22−2−2i2i−2i2i002−22−2-22-220000−22−22−22−222i−2i00000000−i2i2−i2i2i2−i2i2−i2000000000000
χ452-22-2-2-22202002-20-2−22−22−22−222i−2i2i−2i00−22−222-22-20000−22−22−22−222i−2i00000000−i2i2−i2i2−i2i2−i2i2000000000000
χ462-22-2-2-22202002-20-2−22−22−22−222i−2i2i−2i00−22−22-22-2200002−22−22−22−2−2i2i00000000−i2i2−i2i2i2−i2i2−i2000000000000
χ472-22-2-2-22202002-20-2−22−22−22−22−2i2i−2i2i00−22−222-22-20000−22−22−22−22−2i2i00000000i2−i2i2−i2i2−i2i2−i2000000000000
χ482-22-2-2-22202002-20-2−22−22−22−22−2i2i−2i2i00−22−22-22-2200002−22−22−22−22i−2i00000000i2−i2i2−i2−i2i2−i2i2000000000000
χ492-2-2-2222-22-2-2-2222-2000000002i−2i−2i2i2-20000000000002i−2i−2i2i2i−2i−2i2i0000002i−2i000000-222-2000000000000
χ502-2-2-2222-22-2-2-2222-2000000002i−2i−2i2i2-2000000000000−2i2i2i−2i−2i2i2i−2i0000002i−2i0000002-2-22000000000000
χ512-2-2-2222-22-2-2-2222-200000000−2i2i2i−2i2-20000000000002i−2i−2i2i2i−2i−2i2i000000−2i2i0000002-2-22000000000000
χ522-2-2-2222-22-2-2-2222-200000000−2i2i2i−2i2-2000000000000−2i2i2i−2i−2i2i2i−2i000000−2i2i000000-222-2000000000000
χ532-2-2-2222-2-2222-2-2-222-2-222-2-2200002-2-222-20000000000000000000000000000000000002i−2i2i−2i000000
χ542-2-2-2222-2-2222-2-2-222-2-222-2-2200002-2-222-2000000000000000000000000000000000000−2i2i−2i2i000000
χ552-2-2-2222-2-2222-2-2-22-222-2-222-200002-22-2-220000000000000000000000000000000000002i−2i−2i2i000000
χ562-2-2-2222-2-2222-2-2-22-222-2-222-200002-22-2-22000000000000000000000000000000000000−2i2i2i−2i000000
χ572-2-2-2222-2-2-22222-2-22-2-222-2-222i−2i−2i2i-222-2-220000000000000000000000−2i2i002i−2i−2i2i0000000000000000
χ582-2-2-2222-2-2-22222-2-22-2-222-2-22−2i2i2i−2i-222-2-2200000000000000000000002i−2i00−2i2i2i−2i0000000000000000
χ592-2-2-2222-2-2-22222-2-2-222-2-222-22i−2i−2i2i-22-222-20000000000000000000000−2i2i00−2i2i2i−2i0000000000000000
χ602-2-2-2222-2-2-22222-2-2-222-2-222-2−2i2i2i−2i-22-222-200000000000000000000002i−2i002i−2i−2i2i0000000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-40-4400400000000000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ63444-44-4-4-4-40-440040000000000000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ6444-44-4-44-40400-440-42222−22−222222−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ6544-44-4-44-40400-440-4−22−222222−22−2222220000002222−22−220000000000000000000000000000000000000000000000
χ6644-4-4-44-44000000002222−22−22−22−222222000000000000002i2−2i2−2i22i22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6744-4-4-44-44000000002222−22−22−22−22222200000000000000−2i22i22i2−2i2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6844-4-4-44-4400000000−22−2222222222−22−22000000000000002i2−2i2−2i22i2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6944-4-4-44-4400000000−22−2222222222−22−2200000000000000−2i22i22i2−2i22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ704-444-44-4-40000000022−2222−22−2222−2222000000000022−22−222200002-22-2-22-22000000000000000000000000000000
χ714-444-44-4-40000000022−2222−22−2222−22220000000000−222222−220000-22-222-22-2000000000000000000000000000000
χ724-444-44-4-400000000−2222−222222−2222−22000000000022−22−22220000-22-222-22-2000000000000000000000000000000
χ734-444-44-4-400000000−2222−222222−2222−220000000000−222222−2200002-22-2-22-22000000000000000000000000000000
χ744-44-4-4-4440-400-440422−2222−2222−2222−22000000−2222−22220000000000000000000000000000000000000000000000
χ754-44-4-4-4440-400-4404−2222−2222−2222−222200000022−2222−220000000000000000000000000000000000000000000000
χ764-4-444-4-4440-4400-40000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ774-4-444-4-4440-4400-4000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ784-4-444-4-44-404-400404-4-44-444-400000000000000000000000000000000000000000000000000000000
χ794-4-444-4-44-404-40040-444-44-4-4400000000000000000000000000000000000000000000000000000000
χ804-4-4-4444-444-4-4-4-444000000000000-4400000000000000000000000000000000000000000000000000

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