Finite Group Databasebeta

← Group #306809

Character table — Group #306809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-11-111-1-111-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-11111-1
χ91111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-11
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-11-1-1-1-1-1-111-1-111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1111-1-1111111-1-1-1
χ17222222222-22-22-22-20000-2-2222222-2-2000022000000-2-20000000-20000000000000
χ18222222222-22-22-22-20000-2-22222-2-2220000-2-2000000-2-2000000020000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222-2-20000-2-200000022000000020000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-222000022000000220000000-20000000000000
χ2122222222-22-22-22-222222-2-200000000-2-22200-2-2000000220000-200000000000000
χ2222222222-22-22-22-222222-2-200000000-2-2-2-20022000000-2-20000200000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000022220022000000-2-20000-200000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000000022-2-200-2-2000000220000200000000000000
χ252-222-2-2-222-2-222-2-222i2i−2i−2i-22000000002i−2i0000000000000000000000002i−2i00002-20
χ262-222-2-2-222-2-222-2-222i2i−2i−2i-22000000002i−2i000000000000000000000000−2i2i0000-220
χ272-222-2-2-222-2-222-2-22−2i−2i2i2i-2200000000−2i2i0000000000000000000000002i−2i0000-220
χ282-222-2-2-222-2-222-2-22−2i−2i2i2i-2200000000−2i2i000000000000000000000000−2i2i00002-20
χ292-222-2-2-22-222-2-222-20000-2200002-22-2000000002i2i−2i−2i0000000000002i−2i000000000
χ302-222-2-2-22-222-2-222-20000-2200002-22-200000000−2i−2i2i2i000000000000−2i2i000000000
χ312-222-2-2-22-222-2-222-20000-220000-22-22000000002i2i−2i−2i000000000000−2i2i000000000
χ322-222-2-2-22-222-2-222-20000-220000-22-2200000000−2i−2i2i2i0000000000002i−2i000000000
χ332-222-2-2-22-2-222-2-2222i2i−2i−2i2-200002-2-22−2i2i000000000000000000002i−2i00000000000
χ342-222-2-2-22-2-222-2-2222i2i−2i−2i2-20000-222-2−2i2i00000000000000000000−2i2i00000000000
χ352-222-2-2-22-2-222-2-222−2i−2i2i2i2-200002-2-222i−2i00000000000000000000−2i2i00000000000
χ362-222-2-2-22-2-222-2-222−2i−2i2i2i2-20000-222-22i−2i000000000000000000002i−2i00000000000
χ372-22-222-2-20-202020-22i−2i2i−2i00i2i2−i2−i20000002-200002−22−2i2−i22i−2i22−2−20000000000i2−i2000
χ382-22-222-2-20-202020-22i−2i2i−2i00i2i2−i2−i2000000-2200002−22−2i2−i2−2i2i−2−2220000000000−i2i2000
χ392-22-222-2-20-202020-22i−2i2i−2i00−i2−i2i2i20000002-20000−22−22−i2i22i−2i−2−2220000000000−i2i2000
χ402-22-222-2-20-202020-22i−2i2i−2i00−i2−i2i2i2000000-220000−22−22−i2i2−2i2i22−2−20000000000i2−i2000
χ412-22-222-2-20-202020-2−2i2i−2i2i00i2i2−i2−i20000002-20000−22−22i2−i2−2i2i−2−2220000000000i2−i2000
χ422-22-222-2-20-202020-2−2i2i−2i2i00i2i2−i2−i2000000-220000−22−22i2−i22i−2i22−2−20000000000−i2i2000
χ432-22-222-2-20-202020-2−2i2i−2i2i00−i2−i2i2i20000002-200002−22−2−i2i2−2i2i22−2−20000000000−i2i2000
χ442-22-222-2-20-202020-2−2i2i−2i2i00−i2−i2i2i2000000-2200002−22−2−i2i22i−2i−2−2220000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-44-404040-40-44-4-44000000000000000000000000000000000000000000000
χ47444-4-4-44-404040-40-4-444-4000000000000000000000000000000000000000000000
χ48444-4-4-44-40-40-4040400000000000000000000002i2−2i2−2i22i200000000000000000000000
χ49444-4-4-44-40-40-404040000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5044-444-4-4-44040-40-4000000000000000000000000000000000000000000022−2200000
χ5144-444-4-4-44040-40-40000000000000000000000000000000000000000000−222200000
χ5244-444-4-4-4-40-4040400000000000000000004i−4i00000000000000000000000000000
χ5344-444-4-4-4-40-404040000000000000000000−4i4i00000000000000000000000000000
χ5444-4-4-44-440000000000000022−2222−2200000000002i2−2i2000000002i−2i2i−2i000000000000000
χ5544-4-4-44-440000000000000022−2222−220000000000−2i22i200000000−2i2i−2i2i000000000000000
χ5644-4-4-44-4400000000000000−2222−222200000000002i2−2i200000000−2i2i−2i2i000000000000000
χ5744-4-4-44-4400000000000000−2222−22220000000000−2i22i2000000002i−2i2i−2i000000000000000
χ584-444-4-4-4444-4-444-4-400004-40000000000000000000000000000000000000000000
χ594-44-444-4-4040-40-4040000002i22i2−2i2−2i20000000000000000−2i22i2000000000000000000000
χ604-44-444-4-4040-40-404000000−2i2−2i22i22i200000000000000002i2−2i2000000000000000000000
χ614-4-44-444-440-40-40400000004i−4i−4i4i000000000000000000000000000000000000000
χ624-4-44-444-440-40-4040000000−4i4i4i−4i000000000000000000000000000000000000000
χ634-4-44-444-4-404040-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ644-4-44-444-4-404040-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ658-8-8-88-888000000000000000000000000000000000000000000000000000000000

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