Finite Group Databasebeta

← Group #444609

Character table — Group #444609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444222244444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-1-1-1-1-11-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-11-1-1-1-1-11-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111111-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111111-11-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-1-111-111111-1-1-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-1111-111-1-11111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1111-1-1-1111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11-111-1-11-11111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-111-1-1
χ17222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000022-2-2000000002-200000000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000-2-22200000000-2200000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000022-2-200000000-2200000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000-2-222000000002-200000000
χ2122222222-2-2-2-222-2-222-2-222-2-222-2-20000000000000000002200-2-200000200000-20000000000
χ2222222222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000-2-2002200000-20000020000000000
χ2322222222-2-2-2-222-2-222-2-2-2-222-2-2220000000000000000002200-2-200000-20000020000000000
χ2422222222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000-2-2002200000200000-20000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000002200-2-2000000200000-200000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2220000000000000000-2-20022000000-200000200000000000
χ2722222222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000002200-2-2000000-200000200000000000
χ2822222222-2-2-2-2-2-222-2-222-2-22222-2-20000000000000000-2-20022000000200000-200000000000
χ2922-2-22-22-222-2-22-2-2-22-22200000000000000002i2i2i2i−2i−2i−2i−2i002i−2i002i−2i000000000000000000002-2
χ3022-2-22-22-222-2-22-2-2-22-22200000000000000002i2i2i2i−2i−2i−2i−2i00−2i2i00−2i2i00000000000000000000-22
χ3122-2-22-22-222-2-22-2-2-22-2220000000000000000−2i−2i−2i−2i2i2i2i2i002i−2i002i−2i00000000000000000000-22
χ3222-2-22-22-222-2-22-2-2-22-2220000000000000000−2i−2i−2i−2i2i2i2i2i00−2i2i00−2i2i000000000000000000002-2
χ3322-2-22-22-2-2-2222-2222-2-2-2000000002222-2-2-2-200000000002i−2i00−2i2i0000000000000000002i−2i00
χ3422-2-22-22-2-2-2222-2222-2-2-2000000002222-2-2-2-20000000000−2i2i002i−2i000000000000000000−2i2i00
χ3522-2-22-22-2-2-2222-2222-2-2-200000000-2-2-2-2222200000000002i−2i00−2i2i000000000000000000−2i2i00
χ3622-2-22-22-2-2-2222-2222-2-2-200000000-2-2-2-222220000000000−2i2i002i−2i0000000000000000002i−2i00
χ372-22-2-222-22-22-2-2-22-2222-2000000002i2i−2i−2i2i2i−2i−2i000000002i−2i002i−2i00000000000000002-2000000
χ382-22-2-222-22-22-2-2-22-2222-2000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i00−2i2i0000000000000000-22000000
χ392-22-2-222-22-22-2-2-22-2222-200000000−2i−2i2i2i−2i−2i2i2i000000002i−2i002i−2i0000000000000000-22000000
χ402-22-2-222-22-22-2-2-22-2222-200000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i00−2i2i00000000000000002-2000000
χ412-22-2-222-2-22-22222-2-2-22-2000000000000000022-2-222-2-22i−2i00−2i2i0000000000000000002i−2i0000
χ422-22-2-222-2-22-22222-2-2-22-2000000000000000022-2-222-2-2−2i2i002i−2i000000000000000000−2i2i0000
χ432-22-2-222-2-22-22222-2-2-22-20000000000000000-2-222-2-2222i−2i00−2i2i000000000000000000−2i2i0000
χ442-22-2-222-2-22-22222-2-2-22-20000000000000000-2-222-2-222−2i2i002i−2i0000000000000000002i−2i0000
χ452-2-22-2-222-222-22-2-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000002-22-200002i−2i000000000000
χ462-2-22-2-222-222-22-2-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i00000000-22-220000−2i2i000000000000
χ472-2-22-2-222-222-22-2-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000002-22-20000−2i2i000000000000
χ482-2-22-2-222-222-22-2-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000-22-2200002i−2i000000000000
χ492-2-22-2-222-222-2-222-22-2-22000000002i2i−2i−2i−2i−2i2i2i00000000000000002-2-22002i−2i00000000000000
χ502-2-22-2-222-222-2-222-22-2-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000-222-200−2i2i00000000000000
χ512-2-22-2-222-222-2-222-22-2-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000002-2-2200−2i2i00000000000000
χ522-2-22-2-222-222-2-222-22-2-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000-222-2002i−2i00000000000000
χ534444-4-4-4-40000000000004-40000002-22-22-22-22-22-22-22-2000000000000000000000000000000
χ544444-4-4-4-40000000000004-4000000-22-22-22-22-22-22-22-22000000000000000000000000000000
χ554444-4-4-4-4000000000000-440000002-22-22-22-2-22-22-22-22000000000000000000000000000000
χ564444-4-4-4-4000000000000-44000000-22-22-22-222-22-22-22-2000000000000000000000000000000
χ5744-4-44-44-444-4-4-4444-44-4-4000000000000000000000000000000000000000000000000000000
χ5844-4-44-44-4-4-444-44-4-4-4444000000000000000000000000000000000000000000000000000000
χ5944-4-4-44-440000000000000000004i−4i2-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ6044-4-4-44-440000000000000000004i−4i-22-222-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ6144-4-4-44-44000000000000000000−4i4i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ6244-4-4-44-44000000000000000000−4i4i-22-222-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ634-44-44-4-4400000000000000004i−4i002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000
χ644-44-44-4-4400000000000000004i−4i00−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000
χ654-44-44-4-440000000000000000−4i4i002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000
χ664-44-44-4-440000000000000000−4i4i00−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000
χ674-44-4-444-44-44-444-44-4-4-44000000000000000000000000000000000000000000000000000000
χ684-44-4-444-4-44-44-4-4-4444-44000000000000000000000000000000000000000000000000000000
χ694-4-4444-4-4000000000000004-400002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ704-4-4444-4-4000000000000004-40000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ714-4-4444-4-400000000000000-4400002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ724-4-4444-4-400000000000000-440000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ734-4-44-4-4444-4-444-44-4-44-44000000000000000000000000000000000000000000000000000000
χ744-4-44-4-4444-4-44-44-444-44-4000000000000000000000000000000000000000000000000000000

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