Finite Group Databasebeta

← Group #289162

Character table — Group #289162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order12222244444488884448888888888444488888888888888888888882244884488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ9111111111111-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-11-11-11-1
χ10111111111111-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-11-11-11-11
χ11111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111111-11-11-1-11-11
χ12111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-11-11-111-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-11-111-11-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-11-111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-11-111-1-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11-11-1-111-1-11
χ172222222-2-22-2-222222-2-222-2-2-2-22i2i−2i−2i00002i−2i0000000000002i2i−2i−2i00000000000000
χ182222222-2-22-2-222222-2-222-2-2-2-2−2i−2i2i2i0000−2i2i000000000000−2i−2i2i2i00000000000000
χ192222222-2-22-2-2-2-2-2-22-2-2-2-222222i2i−2i−2i00002i−2i000000000000−2i−2i2i2i00000000000000
χ202222222-2-22-2-2-2-2-2-22-2-2-2-22222−2i−2i2i2i0000−2i2i0000000000002i2i−2i−2i00000000000000
χ21222222-222-2220000-2-2-2000000222222-2-2-2-2220000-2-20000000000000000000000
χ22222222-222-2220000-2-2-20000002222-2-222-2-2-2-20000220000000000000000000000
χ23222222-222-2220000-2-2-2000000-2-2-2-222-2-222-2-20000220000000000000000000000
χ24222222-222-2220000-2-2-2000000-2-2-2-2-2-22222220000-2-20000000000000000000000
χ25222222-2-2-2-2-2-20000-2220000002i2i−2i−2i0000−2i2i002i2i−2i−2i000000000022-2-20000000000
χ26222222-2-2-2-2-2-20000-2220000002i2i−2i−2i0000−2i2i00−2i−2i2i2i0000000000-2-2220000000000
χ27222222-2-2-2-2-2-20000-222000000−2i−2i2i2i00002i−2i002i2i−2i−2i0000000000-2-2220000000000
χ28222222-2-2-2-2-2-20000-222000000−2i−2i2i2i00002i−2i00−2i−2i2i2i000000000022-2-20000000000
χ292222-2-222-222-22222-22-2-2-222-2-20000000000000000002222000000000000-2-20000
χ302222-2-222-222-22222-22-2-2-222-2-2000000000000000000-2-2-2-2000000000000220000
χ312222-2-222-222-2-2-2-2-2-22-222-2-22200000000000000000022-2-2000000000000-220000
χ322222-2-222-222-2-2-2-2-2-22-222-2-222000000000000000000-2-2220000000000002-20000
χ332222-2-22-222-222222-2-22-2-2-2-22200000000000000000000000000000022-2-2000000
χ342222-2-22-222-222222-2-22-2-2-2-222000000000000000000000000000000-2-222000000
χ352222-2-22-222-22-2-2-2-2-2-222222-2-20000000000000000000000000000002-2-22000000
χ362222-2-22-222-22-2-2-2-2-2-222222-2-2000000000000000000000000000000-222-2000000
χ372-22-22-202-20-2222−2−20002−22−22−22i−2i2i−2i2-200002i−2i2−22−2000000i2−i2i2−i2i2−i2i2−i20000000000
χ382-22-22-202-20-2222−2−20002−22−22−22i−2i2i−2i-220000−2i2i−22−22000000i2−i2i2−i2−i2i2−i2i20000000000
χ392-22-22-202-20-2222−2−20002−22−22−2−2i2i−2i2i2-20000−2i2i2−22−2000000−i2i2−i2i2−i2i2−i2i20000000000
χ402-22-22-202-20-2222−2−20002−22−22−2−2i2i−2i2i-2200002i−2i−22−22000000−i2i2−i2i2i2−i2i2−i20000000000
χ412-22-22-202-20-22−2−222000−22−22−222i−2i2i−2i2-200002i−2i−22−22000000−i2i2−i2i2−i2i2−i2i20000000000
χ422-22-22-202-20-22−2−222000−22−22−222i−2i2i−2i-220000−2i2i2−22−2000000−i2i2−i2i2i2−i2i2−i20000000000
χ432-22-22-202-20-22−2−222000−22−22−22−2i2i−2i2i2-20000−2i2i−22−22000000i2−i2i2−i2i2−i2i2−i20000000000
χ442-22-22-202-20-22−2−222000−22−22−22−2i2i−2i2i-2200002i−2i2−22−2000000i2−i2i2−i2−i2i2−i2i20000000000
χ452-22-22-20-2202-222−2−20002−2−22−222-2-22002i−2i0000i2−i2−i2i22i−2i00002−2−22−i2i2i2−i20000000000
χ462-22-22-20-2202-222−2−20002−2−22−222-2-2200−2i2i0000−i2i2i2−i2−2i2i00002−2−22i2−i2−i2i20000000000
χ472-22-22-20-2202-222−2−20002−2−22−22-222-2002i−2i0000i2−i2−i2i2−2i2i0000−222−2i2−i2−i2i20000000000
χ482-22-22-20-2202-222−2−20002−2−22−22-222-200−2i2i0000−i2i2i2−i22i−2i0000−222−2−i2i2i2−i20000000000
χ492-22-22-20-2202-2−2−222000−222−22−22-2-22002i−2i0000−i2i2i2−i22i−2i0000−222−2i2−i2−i2i20000000000
χ502-22-22-20-2202-2−2−222000−222−22−22-2-2200−2i2i0000i2−i2−i2i2−2i2i0000−222−2−i2i2i2−i20000000000
χ512-22-22-20-2202-2−2−222000−222−22−2-222-2002i−2i0000−i2i2i2−i2−2i2i00002−2−22−i2i2i2−i20000000000
χ522-22-22-20-2202-2−2−222000−222−22−2-222-200−2i2i0000i2−i2−i2i22i−2i00002−2−22i2−i2−i2i20000000000
χ534444-4-4-44-4-44-400004-440000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-44000044-40000000000000000000000000000000000000000000000
χ5544-4-400400-4004-44-400000000000000000000000000022−2222−22000000000000000000
χ5644-4-400400-4004-44-4000000000000000000000000000−2222−2222000000000000000000
χ5744-4-400400-400-44-4400000000000000000000000000022−22−2222000000000000000000
χ5844-4-400400-400-44-44000000000000000000000000000−222222−22000000000000000000
χ594-44-4-440440-4-42222−22−22000−222222−22−22220000000000000000000000000000000000000000
χ604-44-4-440440-4-4−22−22222200022−22−222222−220000000000000000000000000000000000000000
χ614-44-4-440-4-40442222−22−22000−2222−222222−220000000000000000000000000000000000000000
χ624-44-4-440-4-4044−22−22222200022−2222−22−22220000000000000000000000000000000000000000
χ6388-8-800-80080000000000000000000000000000000000000000000000000000000
χ648-8-880000000042−42−42420000000000000000000000000000000000000000000000000
χ658-8-8800000000−424242−420000000000000000000000000000000000000000000000000

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