Finite Group Databasebeta

← Group #277689

Character table — Group #277689

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111111-1-1-111-1-1-1-1-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-111111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1111-1-111-1-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1-1-1-1111111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-11-1-1-1-1-111-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-111-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-111111-1-1-1-111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-11-1-111-1-111-1-11-1
χ172222222222-2-22-22-2-2-2000022220000-2-2-2-200000000000022-2-2002-200000000000000
χ182222222222-2-22-22-2-2-2000022220000-2-2-2-2000000000000-2-22200-2200000000000000
χ192222222222-2-22-22-2-2-20000-2-2-2-20000222200000000000022-2-200-2200000000000000
χ202222222222-2-22-22-2-2-20000-2-2-2-200002222000000000000-2-222002-200000000000000
χ2122222222-2-222-22-22-2-222220000-2-2-2-2000000000000222200000000-2-2000000000000
χ2222222222-2-222-22-22-2-222220000-2-2-2-2000000000000-2-2-2-20000000022000000000000
χ2322222222-2-222-22-22-2-2-2-2-2-20000222200000000000022-2-200000000-22000000000000
χ2422222222-2-222-22-22-2-2-2-2-2-200002222000000000000-2-222000000002-2000000000000
χ252-22-22-2-22002-2020-20022-2-222−2−2000022−2−22222−2−2−2−22i−2i2i−2i000000000000i2−i2i2−i2000000
χ262-22-22-2-22002-2020-20022-2-222−2−2000022−2−22222−2−2−2−2−2i2i−2i2i000000000000−i2i2−i2i2000000
χ272-22-22-2-22002-2020-20022-2-2−2−2220000−2−222−2−2−2−222222i−2i2i−2i000000000000−i2i2−i2i2000000
χ282-22-22-2-22002-2020-20022-2-2−2−2220000−2−222−2−2−2−22222−2i2i−2i2i000000000000i2−i2i2−i2000000
χ292-22-22-2-22002-2020-200-2-22222−2−2000022−2−2−2−2−2−222222i−2i−2i2i000000000000i2−i2−i2i2000000
χ302-22-22-2-22002-2020-200-2-22222−2−2000022−2−2−2−2−2−22222−2i2i2i−2i000000000000−i2i2i2−i2000000
χ312-22-22-2-22002-2020-200-2-222−2−2220000−2−2222222−2−2−2−22i−2i−2i2i000000000000−i2i2i2−i2000000
χ322-22-22-2-22002-2020-200-2-222−2−2220000−2−2222222−2−2−2−2−2i2i2i−2i000000000000i2−i2−i2i2000000
χ332-2-2-2222-222-2-2-22-222-22-22-2000022-2-2000000000000000000002i−2i00002i−2i0000000000
χ342-2-2-2222-222-2-2-22-222-22-22-2000022-2-200000000000000000000−2i2i0000−2i2i0000000000
χ352-2-2-2222-222-2-2-22-222-2-22-220000-2-222000000000000000000002i−2i0000−2i2i0000000000
χ362-2-2-2222-222-2-2-22-222-2-22-220000-2-22200000000000000000000−2i2i00002i−2i0000000000
χ372-2-2-2222-2-2-2222-22-22-200000000000000002i2i−2i−2i2i2i−2i−2i00002-22-2000000000000002i−2i00
χ382-2-2-2222-2-2-2222-22-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000-22-2200000000000000−2i2i00
χ392-2-2-2222-2-2-2222-22-22-20000000000000000−2i−2i2i2i−2i−2i2i2i00002-22-200000000000000−2i2i00
χ402-2-2-2222-2-2-2222-22-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000-22-22000000000000002i−2i00
χ412-2-2-2222-2-2-2-2-22222-222-22-20000-2-22200000000000000002-2-220000000000002-20000
χ422-2-2-2222-2-2-2-2-22222-222-22-20000-2-2220000000000000000-222-2000000000000-220000
χ432-2-2-2222-2-2-2-2-22222-22-22-22000022-2-200000000000000002-2-22000000000000-220000
χ442-2-2-2222-2-2-2-2-22222-22-22-22000022-2-20000000000000000-222-20000000000002-20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-44-40040-4000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ47444-4-44-4-44-40040-40000000000000000000−2222−2222−2222−222200000000000000000000000000
χ48444-4-44-4-4-4400-40400000004i−4i4i−4i000000000000000000000000000000000000000000
χ49444-4-44-4-4-4400-4040000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5044-444-4-4-4004-40-4040000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5144-444-4-4-4004-40-404000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5244-444-4-4-400-44040-4004-4-440000000000000000000000000000000000000000000000
χ5344-444-4-4-400-44040-400-444-40000000000000000000000000000000000000000000000
χ5444-4-4-4-4440000000000000000002i2−2i22i2−2i222−2222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5544-4-4-4-4440000000000000000002i2−2i22i2−2i2−2222−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5644-4-4-4-444000000000000000000−2i22i2−2i22i222−2222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5744-4-4-4-444000000000000000000−2i22i2−2i22i2−2222−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ584-444-4-44-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i200002-22-2-22-2200000000000000000000000000
χ594-444-4-44-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000-22-222-22-200000000000000000000000000
χ604-444-4-44-400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000-22-222-22-200000000000000000000000000
χ614-444-4-44-400000000000000−2i22i22i2−2i2−2i22i22i2−2i200002-22-2-22-2200000000000000000000000000
χ624-44-44-4-4400-440-4040000002222−22−220000−22−2222220000000000000000000000000000000000
χ634-44-44-4-4400-440-404000000−22−22222200002222−22−220000000000000000000000000000000000
χ644-4-44-44-444-400-4040000000000000004-4-440000000000000000000000000000000000
χ654-4-44-44-444-400-404000000000000000-444-40000000000000000000000000000000000
χ664-4-44-44-44-440040-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ674-4-44-44-44-440040-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ684-4-4-4444-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000

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