Finite Group Databasebeta

← Group #276392

Character table — Group #276392

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888844444888888888888888888882244888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111111-1-1-1-111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-11
χ111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-11
χ121111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-11
χ141111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-11
χ17222222222-2222222-2-22-2-2-2-2-2000000002222222222-20000-2-2-2-200000000000000000000000000
χ18222222222-2222222-2-22-2-2-2-2-20000000022-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-22200000000-2-22222-2-2-2-220000-2-22200000000000000000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-22200000000-2-2-2-2-2-222222000022-2-200000000000000000000000000
χ2122222222-222222-2-222-22-2-2222222-2-2-2-2-2-200000000-222-2-2000000000000000000000000000000
χ2222222222-222222-2-222-22-2-222-2-2-2-22222-2-200000000-2-2-222000000000000000000000000000000
χ2322222222-22-2-2-2-2-2-222-22-2-2-2-22222-2-2-2-222000000002-2-222000000000000000000000000000000
χ2422222222-22-2-2-2-2-2-222-22-2-2-2-2-2-2-2-222222200000000222-2-2000000000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-222-2-200000000-2-200000000200000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ2622222222-2-22222-2-2-2-2-2-222-2-200000000-2-20000000020000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000000002200000000-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000000002200000000-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ292222-2-2-2-22-20000-2-22-2222-2002i2i−2i−2i2i2i−2i−2i00000000000000000002i2i−2i−2i0000000000002-200000000
χ302222-2-2-2-22-20000-2-22-2222-2002i2i−2i−2i2i2i−2i−2i0000000000000000000−2i−2i2i2i000000000000-2200000000
χ312222-2-2-2-22-20000-2-22-2222-200−2i−2i2i2i−2i−2i2i2i00000000000000000002i2i−2i−2i000000000000-2200000000
χ322222-2-2-2-22-20000-2-22-2222-200−2i−2i2i2i−2i−2i2i2i0000000000000000000−2i−2i2i2i0000000000002-200000000
χ332222-2-2-2-2-2-20000222-2-22-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000022-2-200000000002i−2i000000
χ342222-2-2-2-2-2-20000222-2-22-22002i2i−2i−2i−2i−2i2i2i00000000000000000000000-2-2220000000000−2i2i000000
χ352222-2-2-2-2-2-20000222-2-22-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000022-2-20000000000−2i2i000000
χ362222-2-2-2-2-2-20000222-2-22-2200−2i−2i2i2i2i2i−2i−2i00000000000000000000000-2-22200000000002i−2i000000
χ3722-2-2-2-2222022-2-22-200-200000000000002-222-2-222-2-2000000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i200
χ3822-2-2-2-2222022-2-22-200-200000000000002-222-2-222-2-2000000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i200
χ3922-2-2-2-2222022-2-22-200-200000000000002-2-2-222-2-222000000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i200
χ4022-2-2-2-2222022-2-22-200-200000000000002-2-2-222-2-222000000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i200
χ4122-2-2-2-22220-2-2222-200-20000000000000-2222-2-2-2-222000000000i2−i2i2−i2−i2i2−i2i2000000000000i2−i2−i2i200
χ4222-2-2-2-22220-2-2222-200-20000000000000-2222-2-2-2-222000000000−i2i2−i2i2i2−i2i2−i2000000000000−i2i2i2−i200
χ4322-2-2-2-22220-2-2222-200-20000000000000-22-2-22222-2-2000000000i2−i2i2−i2−i2i2−i2i2000000000000−i2i2i2−i200
χ4422-2-2-2-22220-2-2222-200-20000000000000-22-2-22222-2-2000000000−i2i2−i2i2i2−i2i2−i2000000000000i2−i2−i2i200
χ452-22-22-22-2022-22-200-2-202002-200002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i20002i−2ii2−i2i2−i2000000002−22−22−22−20000000000
χ462-22-22-22-2022-22-200-2-202002-200002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i20002i−2i−i2i2−i2i200000000−22−22−22−220000000000
χ472-22-22-22-2022-22-200-2-202002-20000−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000−2i2ii2−i2i2−i200000000−22−22−22−220000000000
χ482-22-22-22-2022-22-200-2-202002-20000−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2000−2i2i−i2i2−i2i2000000002−22−22−22−20000000000
χ492-22-22-22-202-22-2200-2-20200-2200002i−2i2i−2i00i2−i2i2−i2−i2i2−i2i2000−2i2ii2−i2−i2i2000000002−22−2−22−220000000000
χ502-22-22-22-202-22-2200-2-20200-2200002i−2i2i−2i00−i2i2−i2i2i2−i2i2−i2000−2i2i−i2i2i2−i200000000−22−222−22−20000000000
χ512-22-22-22-202-22-2200-2-20200-220000−2i2i−2i2i00i2−i2i2−i2−i2i2−i2i20002i−2ii2−i2−i2i200000000−22−222−22−20000000000
χ522-22-22-22-202-22-2200-2-20200-220000−2i2i−2i2i00−i2i2−i2i2i2−i2i2−i20002i−2i−i2i2i2−i2000000002−22−2−22−220000000000
χ532-22-22-22-20-22-22-200220-200-222-22-2000000i2−i2i2−i2i2−i2i2−i202-200−i2i2−i2i200000000i2−i2−i2i2i2−i2−i2i20000000000
χ542-22-22-22-20-22-22-200220-200-222-22-2000000−i2i2−i2i2−i2i2−i2i202-200i2−i2i2−i200000000−i2i2i2−i2−i2i2i2−i20000000000
χ552-22-22-22-20-22-22-200220-200-22-22-22000000i2−i2i2−i2i2−i2i2−i20-2200−i2i2−i2i200000000−i2i2i2−i2−i2i2i2−i20000000000
χ562-22-22-22-20-22-22-200220-200-22-22-22000000−i2i2−i2i2−i2i2−i2i20-2200i2−i2i2−i200000000i2−i2−i2i2i2−i2−i2i20000000000
χ572-22-22-22-20-2-22-2200220-2002-22-22-2000000i2−i2i2−i2−i2i2−i2i20-2200−i2i2i2−i200000000i2−i2−i2i2−i2i2i2−i20000000000
χ582-22-22-22-20-2-22-2200220-2002-22-22-2000000−i2i2−i2i2i2−i2i2−i20-2200i2−i2−i2i200000000−i2i2i2−i2i2−i2−i2i20000000000
χ592-22-22-22-20-2-22-2200220-2002-2-22-22000000i2−i2i2−i2−i2i2−i2i202-200−i2i2i2−i200000000−i2i2i2−i2i2−i2−i2i20000000000
χ602-22-22-22-20-2-22-2200220-2002-2-22-22000000−i2i2−i2i2i2−i2i2−i202-200i2−i2−i2i200000000i2−i2−i2i2−i2i2i2−i20000000000
χ614444-4-4-4-4440000-4-4-444-4-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-44000044-44-4-44-40000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-4400000-4400-40000000000000000000000000000000022−22−22220000000000000000000000
χ6444-4-444-4-4400000-4400-400000000000000000000000000000000−222222−220000000000000000000000
χ6544-4-444-4-4-4000004-40040000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ6644-4-444-4-4-4000004-4004000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ6744-4-4-4-444-4044-4-4-440040000000000000-440000000000000000000000000000000000000000000
χ6844-4-4-4-444-40-4-444-4400400000000000004-40000000000000000000000000000000000000000000
χ694-44-4-44-44040000004-40-400004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ704-44-4-44-44040000004-40-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ714-44-4-44-440-4000000-4404000000004-4-44000000000000000000000000000000000000000000000
χ724-44-4-44-440-4000000-440400000000-444-4000000000000000000000000000000000000000000000
χ734-4-44-444-4004-4-44000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-44-444-4004-4-4400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-44-444-400-444-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ764-4-44-444-400-444-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ778-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000

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