Finite Group Databasebeta

← Group #307683

Character table — Group #307683

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ311111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-1
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ10111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-1111-1
χ11111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-11-111-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111-1-1-11
χ15111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111111111-11-1-1-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1111-1
χ17222222222-222-2-22-2-2-2000000002222-2-2-2-20022-2-20000000000000000000000
χ18222222222-222-2-22-2-2-20000000022-2-2-2-22200-2-2220000000000000000000000
χ19222222222-222-2-22-2-2-200000000-2-22222-2-200-2-2220000000000000000000000
χ20222222222-222-2-22-2-2-200000000-2-2-2-222220022-2-20000000000000000000000
χ2122222222-22-2-222-22-2-22222222200000000-2-200000000000000-2-20000000000
χ2222222222-22-2-222-22-2-22222-2-2-2-200000000-2-200000000000000220000000000
χ2322222222-22-2-222-22-2-2-2-2-2-222-2-2000000002200000000000000-220000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2-2-2220000000022000000000000002-20000000000
χ252-22-2-222-22-2-2-2222-22-222-2-20000000000002-20000000000002i−2i002i−2i00000000
χ262-22-2-222-22-2-2-2222-22-222-2-20000000000002-2000000000000−2i2i00−2i2i00000000
χ272-22-2-222-22-2-2-2222-22-2-2-222000000000000-220000000000002i−2i00−2i2i00000000
χ282-22-2-222-22-2-2-2222-22-2-2-222000000000000-22000000000000−2i2i002i−2i00000000
χ292-22-2-222-2-2222-2-2-222-200000000002i−2i002i−2i00000022-2-22i2i−2i−2i00000000000000
χ302-22-2-222-2-2222-2-2-222-200000000002i−2i002i−2i000000-2-222−2i−2i2i2i00000000000000
χ312-22-2-222-2-2222-2-2-222-20000000000−2i2i00−2i2i00000022-2-2−2i−2i2i2i00000000000000
χ322-22-2-222-2-2222-2-2-222-20000000000−2i2i00−2i2i000000-2-2222i2i−2i−2i00000000000000
χ332-22-2-222-2-2-22222-2-2-2222-2-20000002i−2i00−2i2i-220000000000000000002i−2i000000
χ342-22-2-222-2-2-22222-2-2-2222-2-2000000−2i2i002i−2i-22000000000000000000−2i2i000000
χ352-22-2-222-2-2-22222-2-2-22-2-2220000002i−2i00−2i2i2-2000000000000000000−2i2i000000
χ362-22-2-222-2-2-22222-2-2-22-2-222000000−2i2i002i−2i2-20000000000000000002i−2i000000
χ372-2-22-22-2202002-20-2002i−2i2i−2i2-22i−2i00000000002−22−20000i2−i2i2−i2000000002−2i2−i200
χ382-2-22-22-2202002-20-2002i−2i2i−2i2-22i−2i0000000000−22−220000−i2i2−i2i200000000−22−i2i200
χ392-2-22-22-2202002-20-2002i−2i2i−2i-22−2i2i00000000002−22−20000i2−i2i2−i200000000−22−i2i200
χ402-2-22-22-2202002-20-2002i−2i2i−2i-22−2i2i0000000000−22−220000−i2i2−i2i2000000002−2i2−i200
χ412-2-22-22-2202002-20-200−2i2i−2i2i2-2−2i2i00000000002−22−20000−i2i2−i2i2000000002−2−i2i200
χ422-2-22-22-2202002-20-200−2i2i−2i2i2-2−2i2i0000000000−22−220000i2−i2i2−i200000000−22i2−i200
χ432-2-22-22-2202002-20-200−2i2i−2i2i-222i−2i00000000002−22−20000−i2i2−i2i200000000−22i2−i200
χ442-2-22-22-2202002-20-200−2i2i−2i2i-222i−2i0000000000−22−220000i2−i2i2−i2000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ4644-44-4-44-4404-400-4000000000000000000000000022−2222−22000000000000000000
χ4744-44-4-44-4404-400-40000000000000000000000000−2222−2222000000000000000000
χ4844-44-4-44-4-40-440040000000000000004i−4i000000000000000000000000000000
χ4944-44-4-44-4-40-44004000000000000000−4i4i000000000000000000000000000000
χ5044-4-444-4-40400-440-4000000000000000000000000000022−22−222200000000000000
χ5144-4-444-4-40400-440-40000000000000000000000000000−222222−2200000000000000
χ5244-4-444-4-40-4004-404004i−4i−4i4i0000000000000000000000000000000000000000
χ5344-4-444-4-40-4004-40400−4i4i4i−4i0000000000000000000000000000000000000000
χ544-44-4-444-444-4-4-4-444-4400000000000000000000000000000000000000000000
χ554-4-44-44-440-400-44040000000000000000000022−22−22220000000000000000000000
χ564-4-44-44-440-400-440400000000000000000000−222222−220000000000000000000000
χ574-4-4-44-44440-4400-4000000000004i−4i0000000000000000000000000000000000
χ584-4-4-44-44440-4400-400000000000−4i4i0000000000000000000000000000000000
χ594-4-4-44-444-404-4004000000000000000000000000022−22−2222000000000000000000
χ604-4-4-44-444-404-40040000000000000000000000000−222222−22000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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