Finite Group Databasebeta

← Group #306367

Character table — Group #306367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-11-111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-111111111-11-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-11111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-2-200002222-2000022220000-2-22200-2-2000000000000-2000000000000
χ18222222222-22-22-22-2-200002222-20000-2-2-2-20000-2-2-2-200220000000000002000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-200002222000022-2-200-2-20000000000002000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-20000-2-2-2-2000022220022000000000000-2000000000000
χ2122222222-22-22-22-22-222220000-222220000-2-2220000-2-2000000000000000-200000000000
χ2222222222-22-22-22-22-222220000-2-2-2-2-20000-2-2-2-2000022000000000000000200000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-22222000022-2-20000-2-2000000000000000200000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-200002222000022000000000000000-200000000000
χ2522-222-2-2-2-20-202020000002i2i−2i−2i022−2−222-2-20000002i−2i2−200i2i2−i2−i2000022−2−20000000000i2−i20
χ2622-222-2-2-2-20-202020000002i2i−2i−2i022−2−2-2-222000000−2i2i2−200i2i2−i2−i20000−2−2220000000000−i2i20
χ2722-222-2-2-2-20-202020000002i2i−2i−2i0−2−22222-2-20000002i−2i−2200−i2−i2i2i20000−2−2220000000000−i2i20
χ2822-222-2-2-2-20-202020000002i2i−2i−2i0−2−222-2-222000000−2i2i−2200−i2−i2i2i2000022−2−20000000000i2−i20
χ2922-222-2-2-2-20-20202000000−2i−2i2i2i022−2−222-2-2000000−2i2i2−200−i2−i2i2i2000022−2−20000000000−i2i20
χ3022-222-2-2-2-20-20202000000−2i−2i2i2i022−2−2-2-2220000002i−2i2−200−i2−i2i2i20000−2−2220000000000i2−i20
χ3122-222-2-2-2-20-20202000000−2i−2i2i2i0−2−22222-2-2000000−2i2i−2200i2i2−i2−i20000−2−2220000000000i2−i20
χ3222-222-2-2-2-20-20202000000−2i−2i2i2i0−2−222-2-2220000002i−2i−2200i2i2−i2−i2000022−2−20000000000−i2i20
χ332-22-222-2-22-2-222-2-22-222-2-200002000000002-200000000002i−2i2i−2i0000000000002i−2i0000000
χ342-22-222-2-22-2-222-2-22-222-2-200002000000002-20000000000−2i2i−2i2i000000000000−2i2i0000000
χ352-22-222-2-22-2-222-2-22-2-2-2220000200000000-2200000000002i−2i2i−2i000000000000−2i2i0000000
χ362-22-222-2-22-2-222-2-22-2-2-2220000200000000-220000000000−2i2i−2i2i0000000000002i−2i0000000
χ372-22-222-2-2-222-2-222-2-200002i−2i2i−2i20000000000002i−2i000000000022-2-200000000002i−2i00000
χ382-22-222-2-2-222-2-222-2-200002i−2i2i−2i20000000000002i−2i0000000000-2-2220000000000−2i2i00000
χ392-22-222-2-2-222-2-222-2-20000−2i2i−2i2i2000000000000−2i2i000000000022-2-20000000000−2i2i00000
χ402-22-222-2-2-222-2-222-2-20000−2i2i−2i2i2000000000000−2i2i0000000000-2-22200000000002i−2i00000
χ412-22-222-2-2-2-222-2-222222-2-22i−2i2i−2i-200000000-2200−2i2i000000000000000000002i−2i000000000
χ422-22-222-2-2-2-222-2-222222-2-2−2i2i−2i2i-200000000-22002i−2i00000000000000000000−2i2i000000000
χ432-22-222-2-2-2-222-2-2222-2-2222i−2i2i−2i-2000000002-200−2i2i00000000000000000000−2i2i000000000
χ442-22-222-2-2-2-222-2-2222-2-222−2i2i−2i2i-2000000002-2002i−2i000000000000000000002i−2i000000000
χ452-2-22-222-202020-20-202i−2i2i−2i000002i−2i2i−2i2−22−2002-20000002−20000i2−i2i2−i2i2−i2i2−i2000000002−2000
χ462-2-22-222-202020-20-202i−2i2i−2i000002i−2i2i−2i−22−22002-2000000−220000−i2i2−i2i2−i2i2−i2i200000000−22000
χ472-2-22-222-202020-20-202i−2i2i−2i00000−2i2i−2i2i2−22−200-220000002−20000i2−i2i2−i2−i2i2−i2i200000000−22000
χ482-2-22-222-202020-20-202i−2i2i−2i00000−2i2i−2i2i−22−2200-22000000−220000−i2i2−i2i2i2−i2i2−i2000000002−2000
χ492-2-22-222-202020-20-20−2i2i−2i2i000002i−2i2i−2i2−22−200-220000002−20000−i2i2−i2i2i2−i2i2−i200000000−22000
χ502-2-22-222-202020-20-20−2i2i−2i2i000002i−2i2i−2i−22−2200-22000000−220000i2−i2i2−i2−i2i2−i2i2000000002−2000
χ512-2-22-222-202020-20-20−2i2i−2i2i00000−2i2i−2i2i2−22−2002-20000002−20000−i2i2−i2i2−i2i2−i2i2000000002−2000
χ522-2-22-222-202020-20-20−2i2i−2i2i00000−2i2i−2i2i−22−22002-2000000−220000i2−i2i2−i2i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-444-4-4-44040-40-4000000000002222−22−22000000000000−2222000000000000000000000000000
χ5544-444-4-4-44040-40-400000000000−22−22222200000000000022−22000000000000000000000000000
χ5644-4-4-44-44040-40-40400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5744-4-4-44-44040-40-4040000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5844-4-4-44-440-404040-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5944-4-4-44-440-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ604-444-4-4-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ614-444-4-4-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ624-444-4-4-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ634-444-4-4-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ644-44-444-4-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ654-4-44-444-40-40-404040000000000000022−2222−220000000000−22220000000000000000000000000
χ664-4-44-444-40-40-4040400000000000000−2222−2222000000000022−220000000000000000000000000
χ674-4-4-44-44440-40-4040000004-4-440000000000000000000000000000000000000000000000
χ684-4-4-44-44440-40-404000000-444-40000000000000000000000000000000000000000000000
χ694-4-4-44-444-404040-4000000000000000000000000000000022−22−2222000000000000000000000
χ704-4-4-44-444-404040-40000000000000000000000000000000−222222−22000000000000000000000
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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