Finite Group Databasebeta

← Group #307352

Character table — Group #307352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888444444888822
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1111-1-111-1-1-11
χ1722222222222-2-2-2-22000000002222-2-200002222-2-2-2-20000000022-2-20000-2-200000000000000000000
χ1822222222222-2-2-2-22000000002222-2-20000-2-2-2-2222200000000-2-2220000-2-200000000000000000000
χ1922222222222-2-2-2-2200000000-2-2-2-2-2-200002222-2-2-2-200000000-2-22200002200000000000000000000
χ2022222222222-2-2-2-2200000000-2-2-2-2-2-20000-2-2-2-222220000000022-2-200002200000000000000000000
χ2122222222-2-2-22222-2222222220000-2-2-2-2-2-20000000000000000000022220000000000-2-20000000000
χ2222222222-2-2-22222-2222222220000-2-2-2-2-2-200000000000000000000-2-2-2-20000000000220000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-20000-2-222220000000000000000000022-2-20000000000-220000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-20000-2-2222200000000000000000000-2-22200000000002-20000000000
χ252222-2-2-2-2-22-2000022222−2−2−2−222-2-20022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i2002i−2i00000022−2−2i2i2−i2−i2000000000000
χ262222-2-2-2-2-22-2000022222−2−2−2−222-2-20022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i200−2i2i00000022−2−2−i2−i2i2i2000000000000
χ272222-2-2-2-2-22-2000022222−2−2−2−2-2-2220022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i200−2i2i000000−2−222−i2−i2i2i2000000000000
χ282222-2-2-2-2-22-2000022222−2−2−2−2-2-2220022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2002i−2i000000−2−222i2i2−i2−i2000000000000
χ292222-2-2-2-2-22-200002−2−2−2−2222222-2-200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i2002i−2i000000−2−222−i2−i2i2i2000000000000
χ302222-2-2-2-2-22-200002−2−2−2−2222222-2-200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i200−2i2i000000−2−222i2i2−i2−i2000000000000
χ312222-2-2-2-2-22-200002−2−2−2−22222-2-22200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i200−2i2i00000022−2−2i2i2−i2−i2000000000000
χ322222-2-2-2-2-22-200002−2−2−2−22222-2-22200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2002i−2i00000022−2−2−i2−i2i2i2000000000000
χ3322-2-22-2-2222-20000-222−2−222−2−22i−2i2i−2i002−22−222-2-2000022−2−222−2−22i−2i00000000i2−i2i2−i2i2−i2i2−i2000000000000
χ3422-2-22-2-2222-20000-222−2−222−2−22i−2i2i−2i002−22−2-2-2220000−2−222−2−222−2i2i00000000i2−i2i2−i2−i2i2−i2i2000000000000
χ3522-2-22-2-2222-20000-222−2−222−2−2−2i2i−2i2i002−22−222-2-2000022−2−222−2−2−2i2i00000000−i2i2−i2i2−i2i2−i2i2000000000000
χ3622-2-22-2-2222-20000-222−2−222−2−2−2i2i−2i2i002−22−2-2-2220000−2−222−2−2222i−2i00000000−i2i2−i2i2i2−i2i2−i2000000000000
χ3722-2-22-2-2222-20000-2−2−222−2−2222i−2i2i−2i00−22−2222-2-20000−2−222−2−2222i−2i00000000−i2i2−i2i2−i2i2−i2i2000000000000
χ3822-2-22-2-2222-20000-2−2−222−2−2222i−2i2i−2i00−22−22-2-222000022−2−222−2−2−2i2i00000000−i2i2−i2i2i2−i2i2−i2000000000000
χ3922-2-22-2-2222-20000-2−2−222−2−222−2i2i−2i2i00−22−2222-2-20000−2−222−2−222−2i2i00000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4022-2-22-2-2222-20000-2−2−222−2−222−2i2i−2i2i00−22−22-2-222000022−2−222−2−22i−2i00000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4122-2-2-222-22-2-222-2-2222-2-2-2-22200002-2-222-20000000000000000000000000000000000002i−2i2i−2i000000
χ4222-2-2-222-22-2-222-2-2222-2-2-2-22200002-2-222-2000000000000000000000000000000000000−2i2i−2i2i000000
χ4322-2-2-222-22-2-222-2-22-2-22222-2-200002-22-2-220000000000000000000000000000000000002i−2i−2i2i000000
χ4422-2-2-222-22-2-222-2-22-2-22222-2-200002-22-2-22000000000000000000000000000000000000−2i2i2i−2i000000
χ4522-2-2-222-2-22222-2-2-222-2-2-2-2222i−2i−2i2i-222-2-220000000000000000000000002i−2i2i−2i−2i2i0000000000000000
χ4622-2-2-222-2-22222-2-2-222-2-2-2-222−2i2i2i−2i-222-2-22000000000000000000000000−2i2i−2i2i2i−2i0000000000000000
χ4722-2-2-222-2-22222-2-2-2-2-22222-2-22i−2i−2i2i-22-222-20000000000000000000000002i−2i−2i2i2i−2i0000000000000000
χ4822-2-2-222-2-22222-2-2-2-2-22222-2-2−2i2i2i−2i-22-222-2000000000000000000000000−2i2i2i−2i−2i2i0000000000000000
χ4922-2-2-222-2-222-2-222-2000000002i−2i−2i2i2-20000000000002i2i−2i−2i−2i−2i2i2i00000000−2i2i0000-222-2000000000000
χ5022-2-2-222-2-222-2-222-2000000002i−2i−2i2i2-2000000000000−2i−2i2i2i2i2i−2i−2i00000000−2i2i00002-2-22000000000000
χ5122-2-2-222-2-222-2-222-200000000−2i2i2i−2i2-20000000000002i2i−2i−2i−2i−2i2i2i000000002i−2i00002-2-22000000000000
χ5222-2-2-222-2-222-2-222-200000000−2i2i2i−2i2-2000000000000−2i−2i2i2i2i2i−2i−2i000000002i−2i0000-222-2000000000000
χ532-22-222-2-20002-22-202-22-22-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200002-22-20000000000000000i2−i2i2−i200
χ542-22-222-2-20002-22-202-22-22-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000-22-220000000000000000−i2i2−i2i200
χ552-22-222-2-20002-22-202-22-22-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200002-22-20000000000000000−i2i2−i2i200
χ562-22-222-2-20002-22-202-22-22-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000-22-220000000000000000i2−i2i2−i200
χ572-22-222-2-20002-22-20-22-22-22-220000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200002-2-220000000000000000i2−i2−i2i200
χ582-22-222-2-20002-22-20-22-22-22-220000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000-222-20000000000000000−i2i2i2−i200
χ592-22-222-2-20002-22-20-22-22-22-220000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200002-2-220000000000000000−i2i2i2−i200
χ602-22-222-2-20002-22-20-22-22-22-220000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000-222-20000000000000000i2−i2−i2i200
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-440000-422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ634444-4-4-4-44-440000-4−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-4-44-4-44-4-44000042222−22−222222−22−22000000−2222−22220000000000000000000000000000000000000000000000
χ6544-4-44-4-44-4-4400004−22−222222−22−22222200000022−2222−220000000000000000000000000000000000000000000000
χ6644-4-4-444-44-4-4-4-4444000000000000-4400000000000000000000000000000000000000000000000000
χ674-44-444-4-4000-44-4400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ684-44-444-4-4000-44-440000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ694-44-4-4-4440000000022−2222−22−2222−22220000000000000022−22−22222-22-2-22-22000000000000000000000000000000
χ704-44-4-4-4440000000022−2222−22−2222−222200000000000000−222222−22-22-222-22-2000000000000000000000000000000
χ714-44-4-4-44400000000−2222−222222−2222−220000000000000022−22−2222-22-222-22-2000000000000000000000000000000
χ724-44-4-4-44400000000−2222−222222−2222−2200000000000000−222222−222-22-2-22-22000000000000000000000000000000
χ734-4-444-44-40000000022−22−222222−22−222200000000002i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ744-4-444-44-40000000022−22−222222−22−22220000000000−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ754-4-444-44-400000000−222222−22−222222−2200000000002i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ764-4-444-44-400000000−222222−22−222222−220000000000−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ774-4-44-44-440004-4-4404-4-44-444-400000000000000000000000000000000000000000000000000000000
χ784-4-44-44-440004-4-440-444-44-4-4400000000000000000000000000000000000000000000000000000000
χ794-4-44-44-44000-444-400000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ804-4-44-44-44000-444-4000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000

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