Finite Group Databasebeta

← Group #99071

Character table — Group #99071

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888844444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1111-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1111-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1111-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1111-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ192222222222-2-2-2222222-20000000022-2-2-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ202222222222-2-2-2222222-20000000022-2-2-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ212222222222-2-2-2-2-2-2-222-200000000-2-22222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-2-2-2-222-200000000-2-22222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-22222222-2-2222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-22222222-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-2-2-22222-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000-2-22222-2-2000000000000000000000000
χ292222-2-2-2-2002-2-222-2-20022i2i2i2i−2i−2i−2i−2i00002-20000002i2i−2i−2i0000000000000000000000000000i2−i2i2−i22−22−2
χ302222-2-2-2-2002-2-222-2-20022i2i2i2i−2i−2i−2i−2i00002-20000002i2i−2i−2i0000000000000000000000000000−i2i2−i2i2−22−22
χ312222-2-2-2-2002-2-222-2-2002−2i−2i−2i−2i2i2i2i2i00002-2000000−2i−2i2i2i0000000000000000000000000000i2−i2i2−i2−22−22
χ322222-2-2-2-2002-2-222-2-2002−2i−2i−2i−2i2i2i2i2i00002-2000000−2i−2i2i2i0000000000000000000000000000−i2i2−i2i22−22−2
χ332222-2-2-2-2002-2-2-2-2220022i2i2i2i−2i−2i−2i−2i0000-22000000−2i−2i2i2i00000000000000000000000000002−2−22−i2i2i2−i2
χ342222-2-2-2-2002-2-2-2-2220022i2i2i2i−2i−2i−2i−2i0000-22000000−2i−2i2i2i0000000000000000000000000000−222−2i2−i2−i2i2
χ352222-2-2-2-2002-2-2-2-222002−2i−2i−2i−2i2i2i2i2i0000-220000002i2i−2i−2i00000000000000000000000000002−2−22i2−i2−i2i2
χ362222-2-2-2-2002-2-2-2-222002−2i−2i−2i−2i2i2i2i2i0000-220000002i2i−2i−2i0000000000000000000000000000−222−2−i2i2i2−i2
χ3722-2-22-22-22i−2i0002i−2i2i−2i2i−2i022−2−222−2−22-200000022−2−2i2−i2i2−i2i2i2−i2−i2002i−2i002-2i2−i2i2−i22−22−20000000000000000
χ3822-2-22-22-22i−2i0002i−2i2i−2i2i−2i022−2−222−2−22-200000022−2−2i2−i2i2−i2i2i2−i2−i200−2i2i00-22−i2i2−i2i2−22−220000000000000000
χ3922-2-22-22-22i−2i0002i−2i2i−2i2i−2i0−2−222−2−2222-2000000−2−222−i2i2−i2i2−i2−i2i2i2002i−2i002-2−i2i2−i2i2−22−220000000000000000
χ4022-2-22-22-22i−2i0002i−2i2i−2i2i−2i0−2−222−2−2222-2000000−2−222−i2i2−i2i2−i2−i2i2i200−2i2i00-22i2−i2i2−i22−22−20000000000000000
χ4122-2-22-22-22i−2i000−2i2i−2i2i2i−2i022−2−222−2−2-22000000−2−222−i2i2−i2i2i2i2−i2−i22-2002i−2i002−2−22−i2i2i2−i20000000000000000
χ4222-2-22-22-22i−2i000−2i2i−2i2i2i−2i022−2−222−2−2-22000000−2−222−i2i2−i2i2i2i2−i2−i2-2200−2i2i00−222−2i2−i2−i2i20000000000000000
χ4322-2-22-22-22i−2i000−2i2i−2i2i2i−2i0−2−222−2−222-2200000022−2−2i2−i2i2−i2−i2−i2i2i22-2002i−2i00−222−2i2−i2−i2i20000000000000000
χ4422-2-22-22-22i−2i000−2i2i−2i2i2i−2i0−2−222−2−222-2200000022−2−2i2−i2i2−i2−i2−i2i2i2-2200−2i2i002−2−22−i2i2i2−i20000000000000000
χ4522-2-22-22-2−2i2i0002i−2i2i−2i−2i2i022−2−222−2−2-22000000−2−222i2−i2i2−i2−i2−i2i2i22-200−2i2i002−2−22i2−i2−i2i20000000000000000
χ4622-2-22-22-2−2i2i0002i−2i2i−2i−2i2i022−2−222−2−2-22000000−2−222i2−i2i2−i2−i2−i2i2i2-22002i−2i00−222−2−i2i2i2−i20000000000000000
χ4722-2-22-22-2−2i2i0002i−2i2i−2i−2i2i0−2−222−2−222-2200000022−2−2−i2i2−i2i2i2i2−i2−i22-200−2i2i00−222−2−i2i2i2−i20000000000000000
χ4822-2-22-22-2−2i2i0002i−2i2i−2i−2i2i0−2−222−2−222-2200000022−2−2−i2i2−i2i2i2i2−i2−i2-22002i−2i002−2−22i2−i2−i2i20000000000000000
χ4922-2-22-22-2−2i2i000−2i2i−2i2i−2i2i022−2−222−2−22-200000022−2−2−i2i2−i2i2−i2−i2i2i2002i−2i00-22i2−i2i2−i2−22−220000000000000000
χ5022-2-22-22-2−2i2i000−2i2i−2i2i−2i2i022−2−222−2−22-200000022−2−2−i2i2−i2i2−i2−i2i2i200−2i2i002-2−i2i2−i2i22−22−20000000000000000
χ5122-2-22-22-2−2i2i000−2i2i−2i2i−2i2i0−2−222−2−2222-2000000−2−222i2−i2i2−i2i2i2−i2−i2002i−2i00-22−i2i2−i2i22−22−20000000000000000
χ5222-2-22-22-2−2i2i000−2i2i−2i2i−2i2i0−2−222−2−2222-2000000−2−222i2−i2i2−i2i2i2−i2−i200−2i2i002-2i2−i2i2−i2−22−220000000000000000
χ532-22-2-2-22222-22-20000-2-222-22-22-22-20000002-2000000002-22-20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ542-22-2-2-22222-22-20000-2-222-22-22-22-20000002-2000000002-22-20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ552-22-2-2-22222-22-20000-2-22-22-22-22-220000002-200000000-22-220000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ562-22-2-2-22222-22-20000-2-22-22-22-22-220000002-200000000-22-220000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ572-22-2-2-222-2-2-22-200002222-22-22-22-2000000-2200000000-22-2200000000000000002−2−222−2−2200000000
χ582-22-2-2-222-2-2-22-200002222-22-22-22-2000000-2200000000-22-220000000000000000−222−2−222−200000000
χ592-22-2-2-222-2-2-22-20000222-22-22-22-22000000-22000000002-22-200000000000000002−2−22−222−200000000
χ602-22-2-2-222-2-2-22-20000222-22-22-22-22000000-22000000002-22-20000000000000000−222−22−2−2200000000
χ614444-4-4-4-400-44444-4-400-4000000000000-440000000000000000000000000000000000000000000000
χ624444-4-4-4-400-444-4-44400-40000000000004-40000000000000000000000000000000000000000000000
χ6344-4-4-44-44000004i−4i−4i4i0002i22i2−2i2−2i2−2i2−2i22i22i2000000000000−222222−22000000000000000000000000000000000000
χ6444-4-4-44-44000004i−4i−4i4i000−2i2−2i22i22i22i22i2−2i2−2i200000000000022−22−2222000000000000000000000000000000000000
χ6544-4-4-44-4400000−4i4i4i−4i0002i22i2−2i2−2i2−2i2−2i22i22i200000000000022−22−2222000000000000000000000000000000000000
χ6644-4-4-44-4400000−4i4i4i−4i000−2i2−2i22i22i22i22i2−2i2−2i2000000000000−222222−22000000000000000000000000000000000000
χ674-44-444-4-40044-4000000-400000000000000004-44-40000000000000000000000000000000000000000
χ684-44-444-4-40044-4000000-40000000000000000-44-440000000000000000000000000000000000000000
χ694-44-444-4-400-4-4400000044i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ704-44-444-4-400-4-440000004−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ714-44-4-4-444444-440000-4-4-400000000000000-4400000000000000000000000000000000000000000000
χ724-44-4-4-444-4-44-44000044-4000000000000004-400000000000000000000000000000000000000000000
χ734-4-444-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i2004i−4i000022−22−22220000000000000000000000000000000000000000
χ744-4-444-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i200−4i4i0000−222222−220000000000000000000000000000000000000000
χ754-4-444-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i2004i−4i0000−222222−220000000000000000000000000000000000000000
χ764-4-444-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i200−4i4i000022−22−22220000000000000000000000000000000000000000
χ774-4-44-444-44i−4i0000000−4i4i022−22−222222−22−222200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ784-4-44-444-44i−4i0000000−4i4i0−222222−22−222222−220000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ794-4-44-444-4−4i4i00000004i−4i022−22−222222−22−22220000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ804-4-44-444-4−4i4i00000004i−4i0−222222−22−222222−2200000000000000002i2−2i2−2i22i200000000000000000000000000000000

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