Finite Group Databasebeta

← Group #306680

Character table — Group #306680

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-11111111111-1-11111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-11111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ111111111111111111-1-1-1-1111111-1-1111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-111-1-111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1111-1-11111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111111-1-1111-1-1-1-1-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-111111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1
χ17222222222-22-22-22-20000-2-222220022-2-22200-2-2000000000000-200000000000000
χ18222222222-22-22-22-20000-2-2222200-2-222-2-200-2-2000000000000200000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-20022-2-2-2-20022000000000000200000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-200-2-222220022000000000000-200000000000000
χ2122222222-22-22-22-222222-2-2000022000000-2-200220000-2-20000000-200000000000
χ2222222222-22-22-22-222222-2-20000-2-2000000-2-200-2-20000220000000200000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220000002200-2-20000220000000-200000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000-2-20000002200220000-2-20000000200000000000
χ252-2-2222-2-22-2-222-2-222i2i−2i−2i-220000000000002i−2i000000000000000000002i−2i00002-20
χ262-2-2222-2-22-2-222-2-222i2i−2i−2i-220000000000002i−2i00000000000000000000−2i2i0000-220
χ272-2-2222-2-22-2-222-2-22−2i−2i2i2i-22000000000000−2i2i000000000000000000002i−2i0000-220
χ282-2-2222-2-22-2-222-2-22−2i−2i2i2i-22000000000000−2i2i00000000000000000000−2i2i00002-20
χ292-2-2222-2-2-222-2-222-20000-220000002-22-2000000002i2i−2i−2i00000002i−2i000000000000
χ302-2-2222-2-2-222-2-222-20000-220000002-22-200000000−2i−2i2i2i0000000−2i2i000000000000
χ312-2-2222-2-2-222-2-222-20000-22000000-22-22000000002i2i−2i−2i0000000−2i2i000000000000
χ322-2-2222-2-2-222-2-222-20000-22000000-22-2200000000−2i−2i2i2i00000002i−2i000000000000
χ332-2-2222-2-2-2-222-2-2222i2i−2i−2i2-20000002-2-2200−2i2i0000000000000000002i−2i000000000
χ342-2-2222-2-2-2-222-2-2222i2i−2i−2i2-2000000-222-200−2i2i000000000000000000−2i2i000000000
χ352-2-2222-2-2-2-222-2-222−2i−2i2i2i2-20000002-2-22002i−2i000000000000000000−2i2i000000000
χ362-2-2222-2-2-2-222-2-222−2i−2i2i2i2-2000000-222-2002i−2i0000000000000000002i−2i000000000
χ372-2-22-2-22202020-20-22i−2i2i−2i0022−2−22i−2i000000002−22-2i2−i2i2−i20022−2−20000000000i2−i2000
χ382-2-22-2-22202020-20-22i−2i2i−2i0022−2−2−2i2i000000002−2-22i2−i2i2−i200−2−2220000000000−i2i2000
χ392-2-22-2-22202020-20-22i−2i2i−2i00−2−2222i−2i00000000−222-2−i2i2−i2i200−2−2220000000000−i2i2000
χ402-2-22-2-22202020-20-22i−2i2i−2i00−2−222−2i2i00000000−22-22−i2i2−i2i20022−2−20000000000i2−i2000
χ412-2-22-2-22202020-20-2−2i2i−2i2i0022−2−22i−2i000000002−2-22−i2i2−i2i200−2−2220000000000i2−i2000
χ422-2-22-2-22202020-20-2−2i2i−2i2i0022−2−2−2i2i000000002−22-2−i2i2−i2i20022−2−20000000000−i2i2000
χ432-2-22-2-22202020-20-2−2i2i−2i2i00−2−2222i−2i00000000−22-22i2−i2i2−i20022−2−20000000000−i2i2000
χ442-2-22-2-22202020-20-2−2i2i−2i2i00−2−222−2i2i00000000−222-2i2−i2i2−i200−2−2220000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ464444-4-4-4-4040-40-40400000000000000000000000022−22−2222000000000000000000000
χ474444-4-4-4-4040-40-404000000000000000000000000−222222−22000000000000000000000
χ484444-4-4-4-40-404040-44-4-44000000000000000000000000000000000000000000000
χ494444-4-4-4-40-404040-4-444-4000000000000000000000000000000000000000000000
χ5044-4-44-44-44040-40-4000000000000000004-40000000000000000000000000000000
χ5144-4-44-44-44040-40-400000000000000000-440000000000000000000000000000000
χ5244-4-44-44-4-40-4040400000000000000000000000000000000000000000002i2−2i200000
χ5344-4-44-44-4-40-404040000000000000000000000000000000000000000000−2i22i200000
χ5444-4-4-44-44000000000000002i2−2i22i2−2i200000000000000000022−222i−2i2i−2i000000000000000
χ5544-4-4-44-44000000000000002i2−2i22i2−2i2000000000000000000−2222−2i2i−2i2i000000000000000
χ5644-4-4-44-4400000000000000−2i22i2−2i22i200000000000000000022−22−2i2i−2i2i000000000000000
χ5744-4-4-44-4400000000000000−2i22i2−2i22i2000000000000000000−22222i−2i2i−2i000000000000000
χ584-44-44-4-4440-40-40400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ594-44-44-4-4440-40-4040000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ604-44-44-4-44-404040-400000004i−4i−4i4i000000000000000000000000000000000000000
χ614-44-44-4-44-404040-40000000−4i4i4i−4i000000000000000000000000000000000000000
χ624-4-4444-4-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ634-4-44-4-4440-40-404040000002222−22−220000000000−2222000000000000000000000000000
χ644-4-44-4-4440-40-40404000000−22−222222000000000022−22000000000000000000000000000
χ658-88-8-888-8000000000000000000000000000000000000000000000000000000000

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