Finite Group Databasebeta

← Group #423509

Character table — Group #423509

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444224488882444448888888888888888882224444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-111-1-1
χ311111111111111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ411111111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-111
χ7111111111111111111111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111
χ911111111111111111111-1-1-1-11111-11111-1111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-111-1-1-1-111
χ1011111111111111111111-1-1-1-11111-11111-1111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-111-1-1-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111-1-1-1-11111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1111111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-1111-1-111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-111-1-1111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-222-2-2000020000-2002i2i−2i−2i0000000000000000000000002i−2i00
χ18222222222222-2-2-2-2-2-2-2-222-2-2000020000-200−2i−2i2i2i000000000000000000000000−2i2i00
χ19222222222222-2-2-2-2-2-2-2-2-2-2220000-200002002i2i−2i−2i000000000000000000000000−2i2i00
χ20222222222222-2-2-2-2-2-2-2-2-2-2220000-20000200−2i−2i2i2i0000000000000000000000002i−2i00
χ2122222222-2-2-2-222-22-2-2-2222220000-222-2-2-20000000000000000002000000-200000000
χ2222222222-2-2-2-222-22-2-2-2222220000-2-2-222-2000000000000000000-2000000200000000
χ2322222222-2-2-2-222-22-2-2-22-2-2-2-20000222-2-22000000000000000000-2000000200000000
χ2422222222-2-2-2-222-22-2-2-22-2-2-2-200002-2-22220000000000000000002000000-200000000
χ2522222222-2-2-2-2-2-22-2222-222-2-22222-200002-2-2000022-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-22-2222-222-2-2-2-2-2-2-200002220000-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-22-2222-2-2-222222220000-2-2-20000-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-22-2222-2-2-222-2-2-2-220000-222000022-2-2000000000000000000000000
χ29222-2-2-2-2222-2-222-2-22-22-2000022-2-20000002-2000000002i2i−2i−2i0000000000000000002i−2i
χ30222-2-2-2-2222-2-222-2-22-22-2000022-2-20000002-200000000−2i−2i2i2i000000000000000000−2i2i
χ31222-2-2-2-2222-2-222-2-22-22-20000-2-222000000-22000000002i2i−2i−2i000000000000000000−2i2i
χ32222-2-2-2-2222-2-222-2-22-22-20000-2-222000000-2200000000−2i−2i2i2i0000000000000000002i−2i
χ33222-2-2-2-22-2-222-2-2-222-222000022-2-2000000-2200000000000022-2-200000000002-20000
χ34222-2-2-2-22-2-222-2-2-222-222000022-2-2000000-22000000000000-2-2220000000000-220000
χ35222-2-2-2-22-2-222-2-2-222-2220000-2-2220000002-200000000000022-2-20000000000-220000
χ36222-2-2-2-22-2-222-2-2-222-2220000-2-2220000002-2000000000000-2-22200000000002-20000
χ372-2-22-22-222-22-22-2222-2-2-200000000000000002i−2i2i−2i00002i−2i2i−2i000002-20000000000000
χ382-2-22-22-222-22-22-2222-2-2-200000000000000002i−2i2i−2i0000−2i2i−2i2i00000-220000000000000
χ392-2-22-22-222-22-22-2222-2-2-20000000000000000−2i2i−2i2i00002i−2i2i−2i00000-220000000000000
χ402-2-22-22-222-22-22-2222-2-2-20000000000000000−2i2i−2i2i0000−2i2i−2i2i000002-20000000000000
χ412-2-22-22-222-22-2-22-2-2-222200000000000000002-2-22000000002-22-20002-200000000000
χ422-2-22-22-222-22-2-22-2-2-222200000000000000002-2-2200000000-22-22000-2200000000000
χ432-2-22-22-222-22-2-22-2-2-22220000000000000000-222-2000000002-22-2000-2200000000000
χ442-2-22-22-222-22-2-22-2-2-22220000000000000000-222-200000000-22-220002-200000000000
χ452-2-2-22-2222-2-222-2-2-222-220000000002-22-2000000000002-2-220000000000002-2000000
χ462-2-2-22-2222-2-222-2-2-222-220000000002-22-200000000000-222-2000000000000-22000000
χ472-2-2-22-2222-2-222-2-2-222-22000000000-22-22000000000002-2-22000000000000-22000000
χ482-2-2-22-2222-2-222-2-2-222-22000000000-22-2200000000000-222-20000000000002-2000000
χ492-2-2-22-222-222-22-22-2-2-2220000000002-2-220000000000000002-2-22000002-2000000000
χ502-2-2-22-222-222-22-22-2-2-2220000000002-2-22000000000000000-222-200000-22000000000
χ512-2-2-22-222-222-22-22-2-2-222000000000-222-20000000000000002-2-2200000-22000000000
χ522-2-2-22-222-222-22-22-2-2-222000000000-222-2000000000000000-222-2000002-2000000000
χ53444-4-4-4-4444-4-4-4-444-44-44000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-444444-4-44-4-4000000000000000000000000000000000000000000000000
χ5544-44-4-44-4000000000000004i−4i2i2−2i22i2−2i20000000000000022−22000000000000000000000000
χ5644-44-4-44-4000000000000004i−4i−2i22i2−2i22i200000000000000−2222000000000000000000000000
χ5744-44-4-44-400000000000000−4i4i2i2−2i22i2−2i200000000000000−2222000000000000000000000000
χ5844-44-4-44-400000000000000−4i4i−2i22i2−2i22i20000000000000022−22000000000000000000000000
χ5944-4-444-4-40000000000004-4002i2−2i2−2i22i20000000000002i2−2i200000000000000000000000000
χ6044-4-444-4-40000000000004-400−2i22i22i2−2i2000000000000−2i22i200000000000000000000000000
χ6144-4-444-4-4000000000000-44002i2−2i2−2i22i2000000000000−2i22i200000000000000000000000000
χ6244-4-444-4-4000000000000-4400−2i22i22i2−2i20000000000002i2−2i200000000000000000000000000
χ634-4-44-44-44-44-444-4-44-444-4000000000000000000000000000000000000000000000000
χ644-4-44-44-44-44-44-444-44-4-44000000000000000000000000000000000000000000000000
χ654-4-4-44-4444-4-44-4444-4-44-4000000000000000000000000000000000000000000000000
χ664-4-4-44-444-444-4-44-4444-4-4000000000000000000000000000000000000000000000000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-888-8000000000000000000000000000000000000000000000000000000000000

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