Finite Group Databasebeta

← Group #264121

Character table — Group #264121

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888822224488888888888888888888224444444488888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-11111-1-1-1-1-1-1-1111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1111-1-1-111-1-1-11
χ172222222222-2-2-222-2222222220000-2-200000000-2-2-2-200000000220000002200000000-200-200000000
χ182222222222-2-2-222-2222222220000-2-200000000-2-2-2-200000000-2-2000000-2-200000000200200000000
χ192222222222-2-2-222-2-2-2-2-2-2-2-2-20000-2-20000000022220000000022000000-2-200000000200-200000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-20000-2-200000000222200000000-2-20000002200000000-200200000000
χ2122222222-2-2222-2-22000000002222-2-22222-2-2-2-200000000000000-2-222-2-20000000000000000000000
χ2222222222-2-2222-2-22000000002222-2-2-2-2-2-2222200000000000000-2-2-2-2220000000000000000000000
χ2322222222-2-2222-2-2200000000-2-2-2-2-2-22222-2-2-2-20000000000000022-2-2220000000000000000000000
χ2422222222-2-2222-2-2200000000-2-2-2-2-2-2-2-2-2-22222000000000000002222-2-20000000000000000000000
χ25222-2-2-2-220022-200-22222−2−2−2−222-2-2002i2i−2i−2i000022−2−2i2i2i2i2−i2−i2−i2−i200002i−2i000022−2−2i2i2−i2−i2000000000000
χ26222-2-2-2-220022-200-22222−2−2−2−222-2-200−2i−2i2i2i000022−2−2−i2−i2−i2−i2i2i2i2i20000−2i2i000022−2−2−i2−i2i2i2000000000000
χ27222-2-2-2-220022-200-22222−2−2−2−2-2-222002i2i−2i−2i000022−2−2i2i2i2i2−i2−i2−i2−i20000−2i2i0000−2−222−i2−i2i2i2000000000000
χ28222-2-2-2-220022-200-22222−2−2−2−2-2-22200−2i−2i2i2i000022−2−2−i2−i2−i2−i2i2i2i2i200002i−2i0000−2−222i2i2−i2−i2000000000000
χ29222-2-2-2-220022-200-2−2−2−2−2222222-2-2002i2i−2i−2i0000−2−222−i2−i2−i2−i2i2i2i2i200002i−2i0000−2−222−i2−i2i2i2000000000000
χ30222-2-2-2-220022-200-2−2−2−2−2222222-2-200−2i−2i2i2i0000−2−222i2i2i2i2−i2−i2−i2−i20000−2i2i0000−2−222i2i2−i2−i2000000000000
χ31222-2-2-2-220022-200-2−2−2−2−22222-2-222002i2i−2i−2i0000−2−222−i2−i2−i2−i2i2i2i2i20000−2i2i000022−2−2i2i2−i2−i2000000000000
χ32222-2-2-2-220022-200-2−2−2−2−22222-2-22200−2i−2i2i2i0000−2−222i2i2i2i2−i2−i2−i2−i200002i−2i000022−2−2−i2−i2i2i2000000000000
χ3322-22-22-2-22-20002-202i2i−2i−2i2i2i−2i−2i000000i2−i2i2−i2i2i2−i2−i2000022−2−222−2−22-20000002i−2i00000000000000i2−i22−200
χ3422-22-22-2-22-20002-202i2i−2i−2i2i2i−2i−2i000000i2−i2i2−i2i2i2−i2−i2000022−2−222−2−2-22000000−2i2i00000000000000−i2i2−2200
χ3522-22-22-2-22-20002-202i2i−2i−2i2i2i−2i−2i000000−i2i2−i2i2−i2−i2i2i20000−2−222−2−2222-20000002i−2i00000000000000−i2i2−2200
χ3622-22-22-2-22-20002-202i2i−2i−2i2i2i−2i−2i000000−i2i2−i2i2−i2−i2i2i20000−2−222−2−222-22000000−2i2i00000000000000i2−i22−200
χ3722-22-22-2-22-20002-20−2i−2i2i2i−2i−2i2i2i000000i2−i2i2−i2i2i2−i2−i20000−2−222−2−2222-2000000−2i2i00000000000000i2−i2−2200
χ3822-22-22-2-22-20002-20−2i−2i2i2i−2i−2i2i2i000000i2−i2i2−i2i2i2−i2−i20000−2−222−2−222-220000002i−2i00000000000000−i2i22−200
χ3922-22-22-2-22-20002-20−2i−2i2i2i−2i−2i2i2i000000−i2i2−i2i2−i2−i2i2i2000022−2−222−2−22-2000000−2i2i00000000000000−i2i22−200
χ4022-22-22-2-22-20002-20−2i−2i2i2i−2i−2i2i2i000000−i2i2−i2i2−i2−i2i2i2000022−2−222−2−2-220000002i−2i00000000000000i2−i2−2200
χ412-2-222-2-2222-222-2-2-2000000002-22-22-20000000000002i−2i2i−2i2i−2i2i−2i002-200000000002i−2i2i−2i000000000000
χ422-2-222-2-2222-222-2-2-2000000002-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i002-20000000000−2i2i−2i2i000000000000
χ432-2-222-2-2222-222-2-2-200000000-22-222-20000000000002i−2i2i−2i2i−2i2i−2i00-220000000000−2i2i−2i2i000000000000
χ442-2-222-2-2222-222-2-2-200000000-22-222-2000000000000−2i2i−2i2i−2i2i−2i2i00-2200000000002i−2i2i−2i000000000000
χ452-2-222-2-22-2-22-2-22222-22-22-22-200002-2000000002-22-20000000000000000000000000002-202-2000000
χ462-2-222-2-22-2-22-2-22222-22-22-22-200002-2000000002-22-2000000000000000000000000000-220-22000000
χ472-2-222-2-22-2-22-2-2222-22-22-22-2200002-200000000-22-220000000000000000000000000002-20-22000000
χ482-2-222-2-22-2-22-2-2222-22-22-22-2200002-200000000-22-22000000000000000000000000000-2202-2000000
χ492-2-222-2-22-2-2-22222-22-22-22-22-22-22-2-2200000000-22-220000000000-220000002-22-20000000000000000
χ502-2-222-2-22-2-2-22222-22-22-22-22-2-22-22-2200000000-22-2200000000002-2000000-22-220000000000000000
χ512-2-222-2-22-2-2-22222-2-22-22-22-222-22-2-22000000002-22-20000000000-22000000-22-220000000000000000
χ522-2-222-2-22-2-2-22222-2-22-22-22-22-22-22-22000000002-22-200000000002-20000002-22-20000000000000000
χ532-2-2-2-222200-22-20022−22−2−22−222-2-220000002-22-2−222−22−22−2−22−220000002-2002−2−222−2−22000000000000
χ542-2-2-2-222200-22-20022−22−2−22−222-2-22000000-22-22−222−2−22−222−22−2000000-22002−2−22−222−2000000000000
χ552-2-2-2-222200-22-20022−22−2−22−22-222-20000002-22-2−222−22−22−2−22−22000000-2200−222−2−222−2000000000000
χ562-2-2-2-222200-22-20022−22−2−22−22-222-2000000-22-22−222−2−22−222−22−20000002-200−222−22−2−22000000000000
χ572-2-2-2-222200-22-2002−22−222−22−22-2-220000002-22-22−2−22−22−222−22−20000002-200−222−2−222−2000000000000
χ582-2-2-2-222200-22-2002−22−222−22−22-2-22000000-22-222−2−222−22−2−22−22000000-2200−222−22−2−22000000000000
χ592-2-2-2-222200-22-2002−22−222−22−2-222-20000002-22-22−2−22−22−222−22−2000000-22002−2−222−2−22000000000000
χ602-2-2-2-222200-22-2002−22−222−22−2-222-2000000-22-222−2−222−22−2−22−220000002-2002−2−22−222−2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-4-4-4400-4-4400422222222−22−22−22−2200000000000000−22−22222200000000000000000000000000000000000000
χ63444-4-4-4-4400-4-44004−22−22−22−2222222222000000000000002222−22−2200000000000000000000000000000000000000
χ6444-44-44-4-4-44000-440000000000000002i2−2i22i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ6544-44-44-4-4-44000-44000000000000000−2i22i2−2i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ6644-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000022−22−222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i2000000−222222−22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i200000022−22−2222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6944-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000−222222−2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ704-444-4-44-44-4000-440000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ714-444-4-44-44-4000-44000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ724-444-4-44-4-440004-404i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ734-444-4-44-4-440004-40−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ744-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000002i2−2i2−2i22i200002-2-22-222-2000000000000000000000000000000
χ754-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000−2i22i22i2−2i20000-222-22-2-22000000000000000000000000000000
χ764-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000002i2−2i2−2i22i20000-222-22-2-22000000000000000000000000000000
χ774-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000−2i22i22i2−2i200002-2-22-222-2000000000000000000000000000000
χ784-4-444-4-44444-4-4-4-44000000000000-4400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444004-4400-422−2222−22−2222−22220000000000000022−22−222200000000000000000000000000000000000000
χ804-4-4-4-4444004-4400-4−2222−222222−2222−2200000000000000−222222−2200000000000000000000000000000000000000

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