Finite Group Databasebeta

← Group #307684

Character table — Group #307684

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888824444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ311111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-11111-1-1
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-111-111-1-11111-1-1
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
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-111-11
χ11111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1111-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-11-1
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1111-1-111-1-1-11
χ16111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-111-11
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
χ2122222222-22-2-222-22-2-22222222200000000-2-2000000000000-200-20000000000
χ2222222222-22-2-222-22-2-22222-2-2-2-200000000-2-200000000000020020000000000
χ2322222222-22-2-222-22-2-2-2-2-2-222-2-20000000022000000000000-20020000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2-2-2220000000022000000000000200-20000000000
χ252-222-2-22-22-2-2-2222-22-222-2-20000000000002-200000000000002i−2i02i−2i00000000
χ262-222-2-22-22-2-2-2222-22-222-2-20000000000002-20000000000000−2i2i0−2i2i00000000
χ272-222-2-22-22-2-2-2222-22-2-2-222000000000000-2200000000000002i−2i0−2i2i00000000
χ282-222-2-22-22-2-2-2222-22-2-2-222000000000000-220000000000000−2i2i02i−2i00000000
χ292-222-2-22-2-2222-2-2-222-200000000002i−2i002i−2i00000022-2-22i2i−2i−2i00000000000000
χ302-222-2-22-2-2222-2-2-222-200000000002i−2i002i−2i000000-2-222−2i−2i2i2i00000000000000
χ312-222-2-22-2-2222-2-2-222-20000000000−2i2i00−2i2i00000022-2-2−2i−2i2i2i00000000000000
χ322-222-2-22-2-2222-2-2-222-20000000000−2i2i00−2i2i000000-2-2222i2i−2i−2i00000000000000
χ332-222-2-22-2-2-22222-2-2-2222-2-20000002i−2i00−2i2i-220000000000000000002i−2i000000
χ342-222-2-22-2-2-22222-2-2-2222-2-2000000−2i2i002i−2i-22000000000000000000−2i2i000000
χ352-222-2-22-2-2-22222-2-2-22-2-2220000002i−2i00−2i2i2-2000000000000000000−2i2i000000
χ362-222-2-22-2-2-22222-2-2-22-2-222000000−2i2i002i−2i2-20000000000000000002i−2i000000
χ372-22-22-2-2202002-20-2002i−2i2i−2i2i−2i2-200000000002−22−20000i2−i2i2−i200000000i2−i22−200
χ382-22-22-2-2202002-20-2002i−2i2i−2i2i−2i2-20000000000−22−220000−i2i2−i2i200000000−i2i2−2200
χ392-22-22-2-2202002-20-2002i−2i2i−2i−2i2i-2200000000002−22−20000i2−i2i2−i200000000−i2i2−2200
χ402-22-22-2-2202002-20-2002i−2i2i−2i−2i2i-220000000000−22−220000−i2i2−i2i200000000i2−i22−200
χ412-22-22-2-2202002-20-200−2i2i−2i2i2i−2i-2200000000002−22−20000−i2i2−i2i200000000i2−i2−2200
χ422-22-22-2-2202002-20-200−2i2i−2i2i2i−2i-220000000000−22−220000i2−i2i2−i200000000−i2i22−200
χ432-22-22-2-2202002-20-200−2i2i−2i2i−2i2i2-200000000002−22−20000−i2i2−i2i200000000−i2i22−200
χ442-22-22-2-2202002-20-200−2i2i−2i2i−2i2i2-20000000000−22−220000i2−i2i2−i200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-44-4-40400-440-4000000000000000000000000000022−22−222200000000000000
χ47444-4-44-4-40400-440-40000000000000000000000000000−222222−2200000000000000
χ48444-4-44-4-40-4004-404004i−4i−4i4i0000000000000000000000000000000000000000
χ49444-4-44-4-40-4004-40400−4i4i4i−4i0000000000000000000000000000000000000000
χ5044-444-4-4-4404-400-4000000000000000000000000022−2222−22000000000000000000
χ5144-444-4-4-4404-400-40000000000000000000000000−2222−2222000000000000000000
χ5244-444-4-4-4-40-440040000000000000004i−4i000000000000000000000000000000
χ5344-444-4-4-4-40-44004000000000000000−4i4i000000000000000000000000000000
χ544-444-4-44-444-4-4-4-444-4400000000000000000000000000000000000000000000
χ554-44-44-4-440-400-44040000000000000000000022−22−22220000000000000000000000
χ564-44-44-4-440-400-440400000000000000000000−222222−220000000000000000000000
χ574-4-44-44-4440-4400-4000000000004i−4i0000000000000000000000000000000000
χ584-4-44-44-4440-4400-400000000000−4i4i0000000000000000000000000000000000
χ594-4-44-44-44-404-4004000000000000000000000000022−22−2222000000000000000000
χ604-4-44-44-44-404-40040000000000000000000000000−222222−22000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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