Finite Group Databasebeta

← Group #310682

Character table — Group #310682

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-111-1-11-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11
χ911111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-11
χ1011111111111111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-11111-1-11-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-11111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-11-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-11111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-111111-1-111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1111
χ17222222222-22-2-222-2-20000-2222222-2-2000022-2-200000000000000-2000000000000
χ18222222222-22-2-222-2-20000-22222-2-2220000-2-2-2-2000000000000002000000000000
χ19222222222-22-2-222-2-20000-2-2-2-2-222220000-2-22200000000000000-2000000000000
χ20222222222-22-2-222-2-20000-2-2-2-2-2-2-2-2-200002222000000000000002000000000000
χ2122222222-22-222-2-22-22222-200000000-2-222000022-2-2000000000000000-20000000
χ2222222222-22-222-2-22-22222-200000000-2-2-2-20000-2-22200000000000000020000000
χ2322222222-22-222-2-22-2-2-2-2-2-20000000022220000-2-222000000000000000-20000000
χ2422222222-22-222-2-22-2-2-2-2-2-20000000022-2-2000022-2-200000000000000020000000
χ252-22-22-22-222-2-2-22-2220000-20000002i−2i00002i−2i00000022-2-20000000002i−2i00000000
χ262-22-22-22-222-2-2-22-2220000-20000002i−2i00002i−2i000000-2-222000000000−2i2i00000000
χ272-22-22-22-222-2-2-22-2220000-2000000−2i2i0000−2i2i00000022-2-2000000000−2i2i00000000
χ282-22-22-22-222-2-2-22-2220000-2000000−2i2i0000−2i2i000000-2-2220000000002i−2i00000000
χ292-22-22-22-22-2-2222-2-2-22i2i−2i−2i20000002i−2i2i−2i00−2i2i000000000000002-20000000000000
χ302-22-22-22-22-2-2222-2-2-22i2i−2i−2i2000000−2i2i2i−2i002i−2i00000000000000-220000000000000
χ312-22-22-22-22-2-2222-2-2-2−2i−2i2i2i20000002i−2i−2i2i00−2i2i00000000000000-220000000000000
χ322-22-22-22-22-2-2222-2-2-2−2i−2i2i2i2000000−2i2i−2i2i002i−2i000000000000002-20000000000000
χ332-22-22-22-2-2-2222-22-222i2i−2i−2i-200000000−2i2i0000000000000000000002-200000002i−2i0
χ342-22-22-22-2-2-2222-22-222i2i−2i−2i-200000000−2i2i000000000000000000000-220000000−2i2i0
χ352-22-22-22-2-2-2222-22-22−2i−2i2i2i-2000000002i−2i0000000000000000000002-20000000−2i2i0
χ362-22-22-22-2-2-2222-22-22−2i−2i2i2i-2000000002i−2i000000000000000000000-2200000002i−2i0
χ372-2-222-2-220202-200-202-22-2022−2−20000002i−2i002−22i−2i002−22−2i2i2−i2−i200000000i2−i200000
χ382-2-222-2-220202-200-202-22-2022−2−2000000−2i2i002−2−2i2i002−22−2−i2−i2i2i200000000−i2i200000
χ392-2-222-2-220202-200-202-22-20−2−2220000002i−2i00−222i−2i00−22−22−i2−i2i2i200000000−i2i200000
χ402-2-222-2-220202-200-202-22-20−2−222000000−2i2i00−22−2i2i00−22−22i2i2−i2−i200000000i2−i200000
χ412-2-222-2-220202-200-20-22-22022−2−20000002i−2i002−2−2i2i00−22−22−i2−i2i2i200000000i2−i200000
χ422-2-222-2-220202-200-20-22-22022−2−2000000−2i2i002−22i−2i00−22−22i2i2−i2−i200000000−i2i200000
χ432-2-222-2-220202-200-20-22-220−2−2220000002i−2i00−22−2i2i002−22−2i2i2−i2−i200000000−i2i200000
χ442-2-222-2-220202-200-20-22-220−2−222000000−2i2i00−222i−2i002−22−2−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ464444-4-4-4-440-400-4400000000000000000000000000000000000000000000022−22000
χ474444-4-4-4-440-400-44000000000000000000000000000000000000000000000−2222000
χ484444-4-4-4-4-404004-4000000000004-40000000000000000000000000000000000000
χ494444-4-4-4-4-404004-400000000000-440000000000000000000000000000000000000
χ5044-4-444-4-4040-4400-40000000000000000000000000022−22−22220000000000000000000
χ5144-4-444-4-4040-4400-400000000000000000000000000−222222−220000000000000000000
χ5244-4-444-4-40-404-400404i−4i−4i4i00000000000000000000000000000000000000000000
χ5344-4-444-4-40-404-40040−4i4i4i−4i00000000000000000000000000000000000000000000
χ5444-4-4-4-4440000000000000022−2222−220000000000000022−2200002-22-2000000000000000
χ5544-4-4-4-4440000000000000022−2222−2200000000000000−22220000-22-22000000000000000
χ5644-4-4-4-44400000000000000−2222−22220000000000000022−220000-22-22000000000000000
χ5744-4-4-4-44400000000000000−2222−222200000000000000−222200002-22-2000000000000000
χ584-44-44-44-4-444-4-4-444-4000040000000000000000000000000000000000000000000
χ594-44-4-44-4440400-4-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ604-44-4-44-4440400-4-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ614-44-4-44-44-40-4004400000004-4-44000000000000000000000000000000000000000
χ624-44-4-44-44-40-400440000000-444-4000000000000000000000000000000000000000
χ634-4-444-4-440-40-440040000002222−22−220000000000−2222000000000000000000000000000
χ644-4-444-4-440-40-44004000000−22−222222000000000022−22000000000000000000000000000
χ658-8-88-888-8000000000000000000000000000000000000000000000000000000000

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