Finite Group Databasebeta

← Group #329809

Character table — Group #329809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222222244444444444444444488888888888888884444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1211111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1311111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222222-2-2-2-22-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-22222-2-2-222-2-2000000000000000022-2-222-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-22222-2-2-222-2-20000000000000000-2-222-2-22200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-2-2-222-2-2-2-22-2-2-2-22-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-22-2-2-2-22-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-22222-2-2-2-2-222000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-22222-22222-2-2-2-2-2220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292222-2-2-2-222-2-22-222-2-220000-200000022-2-222-2-20000000000000000000000002−22−22−22−20000
χ302222-2-2-2-222-2-22-222-2-220000-200000022-2-222-2-2000000000000000000000000−22−22−22−220000
χ312222-2-2-2-222-2-22-222-2-220000-2000000-2-222-2-2220000000000000000000000002−22−2−22−220000
χ322222-2-2-2-222-2-22-222-2-220000-2000000-2-222-2-222000000000000000000000000−22−222−22−20000
χ332222-2-2-2-2-2-2222-2-2-22220000-200000022-2-2-2-2220000000000000000000000002−2−222−2−220000
χ342222-2-2-2-2-2-2222-2-2-22220000-200000022-2-2-2-222000000000000000000000000−222−2−222−20000
χ352222-2-2-2-2-2-2222-2-2-22220000-2000000-2-22222-2-20000000000000000000000002−2−22−222−20000
χ362222-2-2-2-2-2-2222-2-2-22220000-2000000-2-22222-2-2000000000000000000000000−222−22−2−220000
χ3722-2-22-22-22-22-2000000022-2-20002-200i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−2000000000000
χ3822-2-22-22-22-22-2000000022-2-20002-200i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−22000000000000
χ3922-2-22-22-22-22-2000000022-2-20002-200−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−22000000000000
χ4022-2-22-22-22-22-2000000022-2-20002-200−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−2000000000000
χ4122-2-22-22-22-22-20000000-2-222000-2200i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i2000000000000
χ4222-2-22-22-22-22-20000000-2-222000-2200i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i2000000000000
χ4322-2-22-22-22-22-20000000-2-222000-2200−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i2000000000000
χ4422-2-22-22-22-22-20000000-2-222000-2200−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i2000000000000
χ4522-2-22-22-2-22-22000000022-2-2000-2200i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2002i−2i00−2i2i2−22−2−22−22000000000000
χ4622-2-22-22-2-22-22000000022-2-2000-2200i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i200−2i2i002i−2i−22−222−22−2000000000000
χ4722-2-22-22-2-22-22000000022-2-2000-2200−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2002i−2i00−2i2i−22−222−22−2000000000000
χ4822-2-22-22-2-22-22000000022-2-2000-2200−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i200−2i2i002i−2i2−22−2−22−22000000000000
χ4922-2-22-22-2-22-220000000-2-2220002-200i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i22-200-2200i2−i2−i2i2−i2i2i2−i2000000000000
χ5022-2-22-22-2-22-220000000-2-2220002-200i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2-22002-200−i2i2i2−i2i2−i2−i2i2000000000000
χ5122-2-22-22-2-22-220000000-2-2220002-200−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i22-200-2200−i2i2i2−i2i2−i2−i2i2000000000000
χ5222-2-22-22-2-22-220000000-2-2220002-200−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2-22002-200i2−i2−i2i2−i2i2i2−i2000000000000
χ534444-4-4-4-444-4-4-44-4-444-40000400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444-4444-4-4-40000400000000000000000000000000000000000000000000000000
χ5544-4-4-44-444-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ5644-4-4-44-444-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ5744-4-4-44-44-444-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ5844-4-4-44-44-444-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ594-44-44-4-440000004i−4i4i−4i04-44-4000004i−4i00000000000000000000000000000000000000000000
χ604-44-44-4-440000004i−4i4i−4i0-44-4400000−4i4i00000000000000000000000000000000000000000000
χ614-44-44-4-44000000−4i4i−4i4i04-44-400000−4i4i00000000000000000000000000000000000000000000
χ624-44-44-4-44000000−4i4i−4i4i0-44-44000004i−4i00000000000000000000000000000000000000000000
χ634-44-4-444-40000004i−4i−4i4i000000000000000000002i2−2i22i2−2i222−2222−220000000000000000000000000000
χ644-44-4-444-40000004i−4i−4i4i00000000000000000000−2i22i2−2i22i2−2222−22220000000000000000000000000000
χ654-44-4-444-4000000−4i4i4i−4i000000000000000000002i2−2i22i2−2i2−2222−22220000000000000000000000000000
χ664-44-4-444-4000000−4i4i4i−4i00000000000000000000−2i22i2−2i22i222−2222−220000000000000000000000000000
χ674-4-4444-4-40000440000-44-4-44-44-4000000000000000000000000000000000000000000000000
χ684-4-4444-4-40000440000-4-444-4-4-44000000000000000000000000000000000000000000000000
χ694-4-4444-4-40000-4-4000044-4-444-44000000000000000000000000000000000000000000000000
χ704-4-4444-4-40000-4-400004-444-444-4000000000000000000000000000000000000000000000000
χ714-4-44-4-44400004-40000-400004000000000000004-4-4400000000000000000000000000000000
χ724-4-44-4-44400004-40000-40000400000000000000-444-400000000000000000000000000000000
χ734-4-44-4-4440000-44000040000-40000000000000000004i−4i−4i4i0000000000000000000000000000
χ744-4-44-4-4440000-44000040000-4000000000000000000−4i4i4i−4i0000000000000000000000000000

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