Finite Group Databasebeta

← Group #449591

Character table — Group #449591

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12224444222222444444444422222222444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ5111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ8111111111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-1111111-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ1111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ1211111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ1311111111111111111111-1-1-1-1-1-111-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-111-1-1
χ1722222222-2-22-2-2222-2-2-2-222222-200000000002-2000000-2-2000000002-2000000000000
χ1822222222-2-22-2-2222-2-2-2-22222-220000000000-22000000-2-200000000-22000000000000
χ1922222222-2-22-2-2222-2-2-2-2-2-2-2-22-200000000002-20000002200000000-22000000000000
χ2022222222-2-22-2-2222-2-2-2-2-2-2-2-2-220000000000-2200000022000000002-2000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-200002-200000022-2-2-220000000022-2-2000000000000000000
χ222222-2-2-2-2222222-2-2-2-2-2-200002-2000000-2-222-2200000000-2-222000000000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-20000-2200000022-2-22-200000000-2-222000000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-20000-22000000-2-2222-20000000022-2-2000000000000000000
χ252222-2-2-2-22-2-22-2-2222-22-22i2i−2i−2i0000220000000000-2-2002i−2i00000000000000002i−2i0000
χ262222-2-2-2-22-2-22-2-2222-22-22i2i−2i−2i0000-2-2000000000022002i−2i0000000000000000−2i2i0000
χ272222-2-2-2-22-2-22-2-2222-22-2−2i−2i2i2i0000220000000000-2-200−2i2i0000000000000000−2i2i0000
χ282222-2-2-2-22-2-22-2-2222-22-2−2i−2i2i2i0000-2-200000000002200−2i2i00000000000000002i−2i0000
χ292222-2-2-2-2-22-2-22-222-22-222i2i−2i−2i00220000000000-2-20000−2i2i000000000000002i−2i000000
χ302222-2-2-2-2-22-2-22-222-22-222i2i−2i−2i00-2-20000000000220000−2i2i00000000000000−2i2i000000
χ312222-2-2-2-2-22-2-22-222-22-22−2i−2i2i2i00220000000000-2-200002i−2i00000000000000−2i2i000000
χ322222-2-2-2-2-22-2-22-222-22-22−2i−2i2i2i00-2-200000000002200002i−2i000000000000002i−2i000000
χ332222-2-2-2-2-2-22-2-22-2-222220000220000220000-2-20000-2-200000022-2-200000000000000
χ342222-2-2-2-2-2-22-2-22-2-222220000220000-2-20000-2-2000022000000-2-22200000000000000
χ352222-2-2-2-2-2-22-2-22-2-222220000-2-20000220000220000-2-2000000-2-22200000000000000
χ362222-2-2-2-2-2-22-2-22-2-222220000-2-20000-2-200002200002200000022-2-200000000000000
χ372-2-2222-2-2222-2-2-22-22-2-220000002-200000000002-20000002i−2i2i−2i0000002i−2i0000000000
χ382-2-2222-2-2222-2-2-22-22-2-220000002-200000000002-2000000−2i2i−2i2i000000−2i2i0000000000
χ392-2-2222-2-2222-2-2-22-22-2-22000000-220000000000-220000002i−2i2i−2i000000−2i2i0000000000
χ402-2-2222-2-2222-2-2-22-22-2-22000000-220000000000-22000000−2i2i−2i2i0000002i−2i0000000000
χ412-2-2222-2-22-2-2-222-22-2-222000000002-22-2000000002-22-200000000000000000000002-2
χ422-2-2222-2-22-2-2-222-22-2-222000000002-2-22000000002-2-220000000000000000000000-22
χ432-2-2222-2-22-2-2-222-22-2-22200000000-222-200000000-222-20000000000000000000000-22
χ442-2-2222-2-22-2-2-222-22-2-22200000000-22-2200000000-22-2200000000000000000000002-2
χ452-2-22-2-222222-2-2-2-22-222-2000000002-20000000000-2200002i−2i−2i2i000000002i−2i00000000
χ462-2-22-2-222222-2-2-2-22-222-2000000002-20000000000-220000−2i2i2i−2i00000000−2i2i00000000
χ472-2-22-2-222222-2-2-2-22-222-200000000-2200000000002-200002i−2i−2i2i00000000−2i2i00000000
χ482-2-22-2-222222-2-2-2-22-222-200000000-2200000000002-20000−2i2i2i−2i000000002i−2i00000000
χ492-2-22-2-222-22-22-222-2-2-2220000002-2002-2000000-2200-22000000000000000000002-200
χ502-2-22-2-222-22-22-222-2-2-2220000002-200-22000000-22002-200000000000000000000-2200
χ512-2-22-2-222-22-22-222-2-2-222000000-22002-20000002-200-2200000000000000000000-2200
χ522-2-22-2-222-22-22-222-2-2-222000000-2200-220000002-2002-2000000000000000000002-200
χ53444444444-4-44-4-4-4-4-44-44000000000000000000000000000000000000000000000000
χ5444444444-44-4-44-4-4-44-44-4000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i0000000000002+2i−2−2i2−2i−2+2i000000002-22i−2i000000000000002-22i−2i00000000000000
χ5644-4-44i−4i4i−4i0000000000002+2i−2−2i2−2i−2+2i00000000-22−2i2i00000000000000-22−2i2i00000000000000
χ5744-4-44i−4i4i−4i000000000000−2−2i2+2i−2+2i2−2i000000002-22i−2i00000000000000-22−2i2i00000000000000
χ5844-4-44i−4i4i−4i000000000000−2−2i2+2i−2+2i2−2i00000000-22−2i2i000000000000002-22i−2i00000000000000
χ5944-4-4−4i4i−4i4i0000000000002−2i−2+2i2+2i−2−2i000000002-2−2i2i000000000000002-2−2i2i00000000000000
χ6044-4-4−4i4i−4i4i0000000000002−2i−2+2i2+2i−2−2i00000000-222i−2i00000000000000-222i−2i00000000000000
χ6144-4-4−4i4i−4i4i000000000000−2+2i2−2i−2−2i2+2i000000002-2−2i2i00000000000000-222i−2i00000000000000
χ6244-4-4−4i4i−4i4i000000000000−2+2i2−2i−2−2i2+2i00000000-222i−2i000000000000002-2−2i2i00000000000000
χ634-4-4444-4-4-44-44-44-4444-4-4000000000000000000000000000000000000000000000000
χ644-4-4444-4-4-4-4444-44-4-444-4000000000000000000000000000000000000000000000000
χ654-4-44-4-4444-4-4-4444-444-4-4000000000000000000000000000000000000000000000000
χ664-4-44-4-444-4-4444-4-444-4-44000000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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