Finite Group Databasebeta

← Group #10697471

Character table — Group #10697471

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order122222344446664444661212121212121212888812122424242424242424244466121212121212888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ922222222222222-2-2-2-222-2-22222-2-20000-2-20000000000000000000022-2-200000000
χ1022222222222222-2-2-2-222-2-22222-2-20000-2-200000000000000000000-2-22200000000
χ112222222-2-2-2-22222-22-222-2-2-2-2-2-22222-2-22-22222-2-2-2-2000000000000000000000000
χ122222222-2-2-2-22222-22-222-2-2-2-2-2-222-2-2222-2-2-2-2-22222000000000000000000000000
χ132222222-2-2-2-2222-22-222222-2-2-2-2-2-20000-2200000000000000000000000022-2-20000
χ142222222-2-2-2-2222-22-222222-2-2-2-2-2-20000-22000000000000000000000000-2-2220000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-2-2-1-1-12-22-2-1-1111111-1-122-2-2-11-1-1-1-111110000−i3i3−i3i3−i3−i3i3i3000000000000
χ20222222-1-2-2-2-2-1-1-12-22-2-1-1111111-1-122-2-2-11-1-1-1-111110000i3−i3i3−i3i3i3−i3−i3000000000000
χ21222222-1-2-2-2-2-1-1-12-22-2-1-1111111-1-1-2-222-111111-1-1-1-10000−i3i3−i3i3i3i3−i3−i3000000000000
χ22222222-1-2-2-2-2-1-1-12-22-2-1-1111111-1-1-2-222-111111-1-1-1-10000i3−i3i3−i3−i3−i3i3i3000000000000
χ232222-2-2222-2-222222-2-2-2-22222-2-2-2-200002-20000000000000000000000000000002i−2i
χ242222-2-2222-2-222222-2-2-2-22222-2-2-2-200002-2000000000000000000000000000000−2i2i
χ252222-2-2222-2-2222-2-222-2-2-2-222-2-2220000-2200000000002-200002-22-2000000000000
χ262222-2-2222-2-2222-2-222-2-2-2-222-2-2220000-220000000000-220000-22-22000000000000
χ272222-2-22-2-2222222-2-22-2-2-2-2-2-222-2-200002200000000000000000000000000002-200
χ282222-2-22-2-2222222-2-22-2-2-2-2-2-222-2-20000220000000000000000000000000000-2200
χ292222-2-22-2-222222-222-2-2-222-2-222220000-2-2000000002-20022-2-20000000000000000
χ302222-2-22-2-222222-222-2-2-222-2-222220000-2-200000000-2200-2-2220000000000000000
χ312222-2-2-122-2-2-1-1-1-2-2221111-1-111-1-100001-1−i3−i3i3i3−i3−i3i3i3002-2−i3i3i3−i3-11-11000000000000
χ322222-2-2-122-2-2-1-1-1-2-2221111-1-111-1-100001-1−i3−i3i3i3−i3−i3i3i300-22i3−i3−i3i31-11-1000000000000
χ332222-2-2-122-2-2-1-1-1-2-2221111-1-111-1-100001-1i3i3−i3−i3i3i3−i3−i3002-2i3−i3−i3i3-11-11000000000000
χ342222-2-2-122-2-2-1-1-1-2-2221111-1-111-1-100001-1i3i3−i3−i3i3i3−i3−i300-22−i3i3i3−i31-11-1000000000000
χ352222-2-2-1-2-222-1-1-1-222-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i32-200-1-111−i3i3i3−i3000000000000
χ362222-2-2-1-2-222-1-1-1-222-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3-220011-1-1i3−i3−i3i3000000000000
χ372222-2-2-1-2-222-1-1-1-222-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i32-200-1-111i3−i3−i3i3000000000000
χ382222-2-2-1-2-222-1-1-1-222-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3-220011-1-1−i3i3i3−i3000000000000
χ3922-2-22-222-22-2-2-2200002-2002-22-2002−22−2002−22−22−22−2000000000000002i−2i−i2i2−i2i20000
χ4022-2-22-222-22-2-2-2200002-2002-22-2002−22−2002−22−22−22−200000000000000−2i2ii2−i2i2−i20000
χ4122-2-22-222-22-2-2-2200002-2002-22-200−22−2200−22−22−22−22000000000000002i−2ii2−i2i2−i20000
χ4222-2-22-222-22-2-2-2200002-2002-22-200−22−2200−22−22−22−2200000000000000−2i2i−i2i2−i2i20000
χ4322-2-22-22-22-22-2-2200002-200-22-22002−2−22002−22−2−22−220000000000002i−2i00−i2i2i2−i20000
χ4422-2-22-22-22-22-2-2200002-200-22-22002−2−22002−22−2−22−22000000000000−2i2i00i2−i2−i2i20000
χ4522-2-22-22-22-22-2-2200002-200-22-2200−222−200−22−222−22−20000000000002i−2i00i2−i2−i2i20000
χ4622-2-22-22-22-22-2-2200002-200-22-2200−222−200−22−222−22−2000000000000−2i2i00−i2i2i2−i20000
χ47444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200002200000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-2-44-44-2-2-2-222222200002-200000000000000000000000000000000
χ494444-4-4-244-4-4-2-2-244-4-422-2-2-2-222220000-2200000000000000000000000000000000
χ504444-4-4-2-4-444-2-2-24-4-44222222-2-2220000-2-200000000000000000000000000000000
χ5144-4-44-4-24-44-422-20000-2200-22-220022−2222−2200−22−22−22−22000000000000000000000000
χ5244-4-44-4-24-44-422-20000-2200-22-2200−2222−2222002−22−22−22−2000000000000000000000000
χ5344-4-44-4-2-44-4422-20000-22002-22-20022−22−222200−22−222−22−2000000000000000000000000
χ5444-4-44-4-2-44-4422-20000-22002-22-200−222222−22002−22−2−22−22000000000000000000000000
χ5544-4-4-4444-4-44-4-440000-44004-4-440000000000000000000000000000000000000000
χ5644-4-4-444-444-4-4-440000-4400-444-40000000000000000000000000000000000000000
χ5744-4-4-44-24-4-4422-200002-200-222-200000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ5844-4-4-44-24-4-4422-200002-200-222-200000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ5944-4-4-44-2-444-422-200002-2002-2-2200000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ6044-4-4-44-2-444-422-200002-2002-2-2200000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ618-88-800800008-8-80000000000000000000000000000000000000000000000000000
χ628-88-800-40000-444000000000000−4i34i300000000000000000000000000000000000000
χ638-88-800-40000-4440000000000004i3−4i300000000000000000000000000000000000000
χ648-8-880080000-88-80000000000000000000000000000000000000000000000000000
χ658-8-8800-400004-44000000−4i34i300000000000000000000000000000000000000000000
χ668-8-8800-400004-440000004i3−4i300000000000000000000000000000000000000000000

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