Finite Group Databasebeta

← Group #99079

Character table — Group #99079

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
χ911111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222-2-2-2-222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ1922222222222-2-2-2-22222222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2022222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2122222222-2-2-222222222-200000000-2-2-2-222-2-200000000000022-2-222-2-2000000000000000000000000
χ2222222222-2-2-222222222-200000000-2-2-2-222-2-2000000000000-2-222-2-222000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-2-2-22222-2-2-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-2-2-2-22222-20000000022-2-2-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-2-2-2-2-22222-20000000022-2-2-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000-2-22222-2-2000000000000000000000000
χ292222-2-2-2-22-2-2000022-2-222i2i2i2i−2i−2i−2i−2i002-2000000002i2i−2i−2i00000000000000000000i2−i2i2−i22−22−200000000
χ302222-2-2-2-22-2-2000022-2-222i2i2i2i−2i−2i−2i−2i002-2000000002i2i−2i−2i00000000000000000000−i2i2−i2i2−22−2200000000
χ312222-2-2-2-22-2-2000022-2-22−2i−2i−2i−2i2i2i2i2i002-200000000−2i−2i2i2i00000000000000000000i2−i2i2−i2−22−2200000000
χ322222-2-2-2-22-2-2000022-2-22−2i−2i−2i−2i2i2i2i2i002-200000000−2i−2i2i2i00000000000000000000−i2i2−i2i22−22−200000000
χ332222-2-2-2-22-2-20000-2-22222i2i2i2i−2i−2i−2i−2i00-2200000000−2i−2i2i2i000000000000000000002−2−22−i2i2i2−i200000000
χ342222-2-2-2-22-2-20000-2-22222i2i2i2i−2i−2i−2i−2i00-2200000000−2i−2i2i2i00000000000000000000−222−2i2−i2−i2i200000000
χ352222-2-2-2-22-2-20000-2-2222−2i−2i−2i−2i2i2i2i2i00-22000000002i2i−2i−2i000000000000000000002−2−22i2−i2−i2i200000000
χ362222-2-2-2-22-2-20000-2-2222−2i−2i−2i−2i2i2i2i2i00-22000000002i2i−2i−2i00000000000000000000−222−2−i2i2i2−i200000000
χ3722-2-222-2-2-22-222-2-2000022i2i−2i−2i2i2i−2i−2i2-20000002i2i−2i−2i00000000000000000000000000000000i2−i2i2−i22−22−2
χ3822-2-222-2-2-22-222-2-2000022i2i−2i−2i2i2i−2i−2i2-20000002i2i−2i−2i00000000000000000000000000000000−i2i2−i2i2−22−22
χ3922-2-222-2-2-22-222-2-200002−2i−2i2i2i−2i−2i2i2i2-2000000−2i−2i2i2i00000000000000000000000000000000i2−i2i2−i2−22−22
χ4022-2-222-2-2-22-222-2-200002−2i−2i2i2i−2i−2i2i2i2-2000000−2i−2i2i2i00000000000000000000000000000000−i2i2−i2i22−22−2
χ4122-2-222-2-2-22-2-2-222000022i2i−2i−2i2i2i−2i−2i-22000000−2i−2i2i2i000000000000000000000000000000002−2−22−i2i2i2−i2
χ4222-2-222-2-2-22-2-2-222000022i2i−2i−2i2i2i−2i−2i-22000000−2i−2i2i2i00000000000000000000000000000000−222−2i2−i2−i2i2
χ4322-2-222-2-2-22-2-2-22200002−2i−2i2i2i−2i−2i2i2i-220000002i2i−2i−2i000000000000000000000000000000002−2−22i2−i2−i2i2
χ4422-2-222-2-2-22-2-2-22200002−2i−2i2i2i−2i−2i2i2i-220000002i2i−2i−2i00000000000000000000000000000000−222−2−i2i2i2−i2
χ452-22-22-22-20002i−2i2i−2i2i−2i2i−2i02−22−22−22−200002-200i2−i2i2−i2i2−i2i2−i222−2−2002i−2i002-2i2−i2i2−i22−22−20000000000000000
χ462-22-22-22-20002i−2i2i−2i2i−2i2i−2i02−22−22−22−200002-200i2−i2i2−i2i2−i2i2−i222−2−200−2i2i00-22−i2i2−i2i2−22−220000000000000000
χ472-22-22-22-20002i−2i2i−2i2i−2i2i−2i0−22−22−22−2200002-200−i2i2−i2i2−i2i2−i2i2−2−222002i−2i002-2−i2i2−i2i2−22−220000000000000000
χ482-22-22-22-20002i−2i2i−2i2i−2i2i−2i0−22−22−22−2200002-200−i2i2−i2i2−i2i2−i2i2−2−22200−2i2i00-22i2−i2i2−i22−22−20000000000000000
χ492-22-22-22-20002i−2i2i−2i−2i2i−2i2i02−22−22−22−20000-2200i2−i2i2−i2−i2i2−i2i2−2−2222-2002i−2i002−2−22−i2i2i2−i20000000000000000
χ502-22-22-22-20002i−2i2i−2i−2i2i−2i2i02−22−22−22−20000-2200i2−i2i2−i2−i2i2−i2i2−2−222-2200−2i2i00−222−2i2−i2−i2i20000000000000000
χ512-22-22-22-20002i−2i2i−2i−2i2i−2i2i0−22−22−22−220000-2200−i2i2−i2i2i2−i2i2−i222−2−22-2002i−2i00−222−2i2−i2−i2i20000000000000000
χ522-22-22-22-20002i−2i2i−2i−2i2i−2i2i0−22−22−22−220000-2200−i2i2−i2i2i2−i2i2−i222−2−2-2200−2i2i002−2−22−i2i2i2−i20000000000000000
χ532-22-22-22-2000−2i2i−2i2i2i−2i2i−2i02−22−22−22−20000-2200−i2i2−i2i2i2−i2i2−i2−2−2222-200−2i2i002−2−22i2−i2−i2i20000000000000000
χ542-22-22-22-2000−2i2i−2i2i2i−2i2i−2i02−22−22−22−20000-2200−i2i2−i2i2i2−i2i2−i2−2−222-22002i−2i00−222−2−i2i2i2−i20000000000000000
χ552-22-22-22-2000−2i2i−2i2i2i−2i2i−2i0−22−22−22−220000-2200i2−i2i2−i2−i2i2−i2i222−2−22-200−2i2i00−222−2−i2i2i2−i20000000000000000
χ562-22-22-22-2000−2i2i−2i2i2i−2i2i−2i0−22−22−22−220000-2200i2−i2i2−i2−i2i2−i2i222−2−2-22002i−2i002−2−22i2−i2−i2i20000000000000000
χ572-22-22-22-2000−2i2i−2i2i−2i2i−2i2i02−22−22−22−200002-200−i2i2−i2i2−i2i2−i2i222−2−2002i−2i00-22i2−i2i2−i2−22−220000000000000000
χ582-22-22-22-2000−2i2i−2i2i−2i2i−2i2i02−22−22−22−200002-200−i2i2−i2i2−i2i2−i2i222−2−200−2i2i002-2−i2i2−i2i22−22−20000000000000000
χ592-22-22-22-2000−2i2i−2i2i−2i2i−2i2i0−22−22−22−2200002-200i2−i2i2−i2i2−i2i2−i2−2−222002i−2i00-22−i2i2−i2i22−22−20000000000000000
χ602-22-22-22-2000−2i2i−2i2i−2i2i−2i2i0−22−22−22−2200002-200i2−i2i2−i2i2−i2i2−i2−2−22200−2i2i002-2i2−i2i2−i2−22−220000000000000000
χ614444-4-4-4-4-444000044-4-4-40000000000-44000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4440000-4-444-400000000004-4000000000000000000000000000000000000000000000000
χ6344-4-444-4-44-4444-4-40000-400000000-4400000000000000000000000000000000000000000000000000
χ6444-4-444-4-44-44-4-4440000-4000000004-400000000000000000000000000000000000000000000000000
χ6544-4-4-4-44444-400000000-40000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6644-4-4-4-44444-400000000-4000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ6744-4-4-4-444-4-4400000000444-4-4-4-4440000000000000000000000000000000000000000000000000000
χ6844-4-4-4-444-4-44000000004-4-44444-4-40000000000000000000000000000000000000000000000000000
χ694-44-4-44-4400000004i−4i−4i4i02i2−2i22i2−2i2−2i22i2−2i22i2000000000000−222222−22000000000000000000000000000000000000
χ704-44-4-44-4400000004i−4i−4i4i0−2i22i2−2i22i22i2−2i22i2−2i200000000000022−22−2222000000000000000000000000000000000000
χ714-44-4-44-440000000−4i4i4i−4i02i2−2i22i2−2i2−2i22i2−2i22i200000000000022−22−2222000000000000000000000000000000000000
χ724-44-4-44-440000000−4i4i4i−4i0−2i22i2−2i22i22i2−2i22i2−2i2000000000000−222222−22000000000000000000000000000000000000
χ734-4-444-4-440004i−4i−4i4i000002i2−2i2−2i22i22i2−2i2−2i22i200000000−222222−220000000000000000000000000000000000000000
χ744-4-444-4-440004i−4i−4i4i00000−2i22i22i2−2i2−2i22i22i2−2i20000000022−22−22220000000000000000000000000000000000000000
χ754-4-444-4-44000−4i4i4i−4i000002i2−2i2−2i22i22i2−2i2−2i22i20000000022−22−22220000000000000000000000000000000000000000
χ764-4-444-4-44000−4i4i4i−4i00000−2i22i22i2−2i2−2i22i22i2−2i200000000−222222−220000000000000000000000000000000000000000
χ774-4-44-444-400000000000022−22−2222−222222−220000004i−4i000000002i2−2i2−2i22i200000000000000000000000000000000
χ784-4-44-444-400000000000022−22−2222−222222−22000000−4i4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ794-4-44-444-4000000000000−222222−2222−22−22220000004i−4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ804-4-44-444-4000000000000−222222−2222−22−2222000000−4i4i000000002i2−2i2−2i22i200000000000000000000000000000000

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