Finite Group Databasebeta

← Group #348774

Character table — Group #348774

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444444444444422444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-11-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-11-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-111111-1-11111-1-1-1-1111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-1-1-111111-1-11111-1-1-1-1111-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-1-111111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ17222222222222222-2-2-2-222222-2-2-222222200000000-200-2-2-200-2-200000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-22200000000-200-222002200000000000000000000000000
χ19222222222222-2-2-22222-2000022-20000-2-222222222-2-2-2-200-2-20000000000000000000000000000
χ20222222222222-2-2-22222-2000022-20000-2-2-2-2-2-2-2-2-2-2-222-200220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000-2-220000-2-200000000200200000022-2-222-2-2000000000000000000
χ22222222222222-2-2-2-2-2-2-2-20000-2-220000-2-2000000002002000000-2-222-2-222000000000000000000
χ2322222222-2-2-2-2222-2-2-2-22222222-2-2-2-2-2-2-200000000-20022200-2-200000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-2-2-222-22222-2-200000000-2002-2-2002200000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-20000-2-2-20000222222-2-2-2-2-2-2-2200220000000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-20000-2-2-2000022-2-2-2-22222-222200-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022200002200000000200-200000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000022200002200000000200-2000000-2-22222-2-2000000000000000000
χ2922-2-2-222-22i2i−2i−2i0002-22-2000002i−2i00000002i2i−2i−2i22-2-200000000000000000022−2−2i2i2−i2−i20000i2−i22−200
χ3022-2-2-222-22i2i−2i−2i0002-22-2000002i−2i00000002i2i−2i−2i22-2-2000000000000000000−2−222−i2−i2i2i20000−i2i2−2200
χ3122-2-2-222-22i2i−2i−2i0002-22-2000002i−2i0000000−2i−2i2i2i-2-22200000000000000000022−2−2i2i2−i2−i20000−i2i2−2200
χ3222-2-2-222-22i2i−2i−2i0002-22-2000002i−2i0000000−2i−2i2i2i-2-222000000000000000000−2−222−i2−i2i2i20000i2−i22−200
χ3322-2-2-222-2−2i−2i2i2i0002-22-200000−2i2i00000002i2i−2i−2i-2-22200000000000000000022−2−2−i2−i2i2i20000i2−i2−2200
χ3422-2-2-222-2−2i−2i2i2i0002-22-200000−2i2i00000002i2i−2i−2i-2-222000000000000000000−2−222i2i2−i2−i20000−i2i22−200
χ3522-2-2-222-2−2i−2i2i2i0002-22-200000−2i2i0000000−2i−2i2i2i22-2-200000000000000000022−2−2−i2−i2i2i20000−i2i22−200
χ3622-2-2-222-2−2i−2i2i2i0002-22-200000−2i2i0000000−2i−2i2i2i22-2-2000000000000000000−2−222i2i2−i2−i20000i2−i2−2200
χ372-2-22-22-22000022-222-2-2-2000000-22i2i−2i−2i0000002i−2i2i−2i20002i−2i2i−2i002-22-20000000000000000000000
χ382-2-22-22-22000022-222-2-2-2000000-22i2i−2i−2i000000−2i2i−2i2i20002i−2i−2i2i00-22-220000000000000000000000
χ392-2-22-22-22000022-222-2-2-2000000-2−2i−2i2i2i0000002i−2i2i−2i2000−2i2i2i−2i00-22-220000000000000000000000
χ402-2-22-22-22000022-222-2-2-2000000-2−2i−2i2i2i000000−2i2i−2i2i2000−2i2i−2i2i002-22-20000000000000000000000
χ412-2-22-22-22000022-2-2-222-200000022i2i−2i−2i002-22-20000-22-20−2i2i000000002i−2i2i−2i000000000000000000
χ422-2-22-22-22000022-2-2-222-200000022i2i−2i−2i00-22-220000-2-220−2i2i00000000−2i2i−2i2i000000000000000000
χ432-2-22-22-22000022-2-2-222-20000002−2i−2i2i2i002-22-20000-22-202i−2i00000000−2i2i−2i2i000000000000000000
χ442-2-22-22-22000022-2-2-222-20000002−2i−2i2i2i00-22-220000-2-2202i−2i000000002i−2i2i−2i000000000000000000
χ452-2-22-22-220000-2-2222-2-2222-2-200200000000002i−2i2i−2i-200000−2i2i2-200002i−2i−2i2i000000000000000000
χ462-2-22-22-220000-2-2222-2-2222-2-20020000000000−2i2i−2i2i-2000002i−2i2-20000−2i2i2i−2i000000000000000000
χ472-2-22-22-220000-2-2222-2-22-2-22200200000000002i−2i2i−2i-200000−2i2i-220000−2i2i2i−2i000000000000000000
χ482-2-22-22-220000-2-2222-2-22-2-2220020000000000−2i2i−2i2i-2000002i−2i-2200002i−2i−2i2i000000000000000000
χ492-2-22-22-220000-2-22-2-222222-2-200-20000002-22-200002-2200000-222-2-220000000000000000000000
χ502-2-22-22-220000-2-22-2-222222-2-200-2000000-22-22000022-200000-22-222-20000000000000000000000
χ512-2-22-22-220000-2-22-2-2222-2-22200-20000002-22-200002-22000002-2-222-20000000000000000000000
χ522-2-22-22-220000-2-22-2-2222-2-22200-2000000-22-22000022-2000002-22-2-220000000000000000000000
χ532-2-2-22-2222-22-22-220000-22-22-20002-22-22-200000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ542-2-2-22-2222-22-22-220000-22-22-20002-22-22-200000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ552-2-2-22-2222-22-22-220000-2-22-22000-22-222-200000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000
χ562-2-2-22-2222-22-22-220000-2-22-22000-22-222-200000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000
χ572-2-2-22-222-22-222-220000-22-22-2000-22-22-2200000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2000000
χ582-2-2-22-222-22-222-220000-22-22-2000-22-22-2200000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2000000
χ592-2-2-22-222-22-222-220000-2-22-220002-22-2-2200000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2000000
χ602-2-2-22-222-22-222-220000-2-22-220002-22-2-2200000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2000000
χ61444-4-4-4-4400004-4-40000400000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ62444-4-4-4-4400004-4-4000040000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ63444-4-4-4-440000-4440000-44-4-4400000000000000000000000000000000000000000000000000000
χ64444-4-4-4-440000-4440000-4-444-400000000000000000000000000000000000000000000000000000
χ6544-4-4-444-44i4i−4i−4i000-44-4400000−4i4i000000000000000000000000000000000000000000000000000
χ6644-4-4-444-4−4i−4i4i4i000-44-44000004i−4i000000000000000000000000000000000000000000000000000
χ674-444-4-44-44i−4i−4i4i000000000000000000000000000000000000000000000002i−2i−2i2i-222-20000000000
χ684-444-4-44-44i−4i−4i4i00000000000000000000000000000000000000000000000−2i2i2i−2i2-2-220000000000
χ694-444-4-44-4−4i4i4i−4i000000000000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000
χ704-444-4-44-4−4i4i4i−4i00000000000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000
χ714-44-444-4-400000004-4-440000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ724-44-444-4-400000004-4-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ734-44-444-4-40000000-444-4000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ744-44-444-4-40000000-444-400000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ754-4-4-44-4444-44-4-44-40000400000000000-4400000000000000000000000000000000000000000000
χ764-4-4-44-444-44-44-44-400004000000000004-400000000000000000000000000000000000000000000
χ7788-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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