Finite Group Databasebeta

← Group #10695633

Character table — Group #10695633

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222222234466644466666612121212888812122424242424242424224466661212121244444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1-1-111
χ922222222222-2-2222-2-2-2222222-2-2-2-20000-2-200000000000000000000000022-2-2000000
χ1022222222222-2-2222-2-2-2222222-2-2-2-20000-2-2000000000000000000000000-2-222000000
χ112222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ122222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ132222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111112-22-2-1-111-1-11100000000000000
χ142222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-22-2211-1-111-1-100000000000000
χ15222222-2-2-2-2222222-2-2222-2-2-2-2-2-22200002-200000000020-2002200-2-200000000000000
χ16222222-2-2-2-2222222-2-2222-2-2-2-2-2-22200002-2000000000-20200-2-2002200000000000000
χ17222222-2-2-2-22-2-222222-222-2-2-2-222-2-20000-22000000000000000000000000000000002i−2i
χ18222222-2-2-2-22-2-222222-222-2-2-2-222-2-20000-2200000000000000000000000000000000−2i2i
χ19222222-2-2-2-2-122-1-1-1-2-22-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i3020-2−i3i3-1-1−i3i31100000000000000
χ20222222-2-2-2-2-122-1-1-1-2-22-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i30-202i3−i311i3−i3-1-100000000000000
χ21222222-2-2-2-2-122-1-1-1-2-22-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i3020-2i3−i3-1-1i3−i31100000000000000
χ22222222-2-2-2-2-122-1-1-1-2-22-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i30-202−i3i311−i3i3-1-100000000000000
χ232222-2-22-2-222222222-2-2-2-222-2-2222222-2-2-2-222-2-222-2-200000000000000000000000000
χ242222-2-22-2-222222222-2-2-2-222-2-22222-2-222-2-2-2-222-2-22200000000000000000000000000
χ252222-2-22-2-222-2-2222-222-2-222-2-2-2-2-2-2000022000000000000000000000000000022-2-200
χ262222-2-22-2-222-2-2222-222-2-222-2-2-2-2-2-20000220000000000000000000000000000-2-22200
χ272222-2-22-2-22-122-1-1-12-2-211-1-111-1-1-1-122-2-211-1-111-1-1110000−i3i3−i3i3i3−i3−i3i300000000000000
χ282222-2-22-2-22-122-1-1-12-2-211-1-111-1-1-1-122-2-211-1-111-1-1110000i3−i3i3−i3−i3i3i3−i300000000000000
χ292222-2-22-2-22-122-1-1-12-2-211-1-111-1-1-1-1-2-2221111-1-111-1-10000−i3i3i3−i3i3−i3i3−i300000000000000
χ302222-2-22-2-22-122-1-1-12-2-211-1-111-1-1-1-1-2-2221111-1-111-1-10000i3−i3−i3i3−i3i3−i3i300000000000000
χ312222-2-2-222-2222222-22-2-2-2-2-222-2-2220000-220000000020-202200-2-20000000000000000
χ322222-2-2-222-2222222-22-2-2-2-2-222-2-2220000-2200000000-2020-2-200220000000000000000
χ332222-2-2-222-22-2-22222-22-2-2-2-22222-2-200002-20000000000000000000022-2-20000000000
χ342222-2-2-222-22-2-22222-22-2-2-2-22222-2-200002-200000000000000000000-2-2220000000000
χ352222-2-2-222-2-122-1-1-1-22-21111-1-111-1-100001-1−i3−i3i3i3i3i3−i3−i320-20-1-1−i3i311i3−i300000000000000
χ362222-2-2-222-2-122-1-1-1-22-21111-1-111-1-100001-1−i3−i3i3i3i3i3−i3−i3-202011i3−i3-1-1−i3i300000000000000
χ372222-2-2-222-2-122-1-1-1-22-21111-1-111-1-100001-1i3i3−i3−i3−i3−i3i3i320-20-1-1i3−i311−i3i300000000000000
χ382222-2-2-222-2-122-1-1-1-22-21111-1-111-1-100001-1i3i3−i3−i3−i3−i3i3i3-202011−i3i3-1-1i3−i300000000000000
χ392-22-22-222-2-2200-2-220002-22-22-200002−22−2002−22−22−22−20000000000000000002i−2i−i2i2−i2i200
χ402-22-22-222-2-2200-2-220002-22-22-200002−22−2002−22−22−22−2000000000000000000−2i2ii2−i2i2−i200
χ412-22-22-222-2-2200-2-220002-22-22-20000−22−2200−22−22−22−220000000000000000002i−2ii2−i2i2−i200
χ422-22-22-222-2-2200-2-220002-22-22-20000−22−2200−22−22−22−22000000000000000000−2i2i−i2i2−i2i200
χ432-22-2-222-22-2200-2-22000-222-2-2200002−2−22002−2−222−2−2200000000000000002i−2i00−i2i2i2−i200
χ442-22-2-222-22-2200-2-22000-222-2-2200002−2−22002−2−222−2−220000000000000000−2i2i00i2−i2−i2i200
χ452-22-2-222-22-2200-2-22000-222-2-220000−222−200−222−2−222−200000000000000002i−2i00i2−i2−i2i200
χ462-22-2-222-22-2200-2-22000-222-2-220000−222−200−222−2−222−20000000000000000−2i2i00−i2i2i2−i200
χ474444444444-2-4-4-2-2-2-4-4-4-2-2-2-2-2-222220000220000000000000000000000000000000000
χ48444444-4-4-4-4-2-4-4-2-2-244-4-2-22222-2-22200002-20000000000000000000000000000000000
χ494444-4-44-4-44-2-4-4-2-2-2-44422-2-22222220000-2-20000000000000000000000000000000000
χ504444-4-4-444-4-2-4-4-2-2-24-442222-2-2-2-2220000-220000000000000000000000000000000000
χ5144-4-400000044-4-44-4000000000004-4000000000000000000000000002i−2i2i−2i0000000000
χ5244-4-400000044-4-44-4000000000004-400000000000000000000000000−2i2i−2i2i0000000000
χ5344-4-40000004-44-44-400000000000-44000000000000000000000000002i−2i−2i2i0000000000
χ5444-4-40000004-44-44-400000000000-4400000000000000000000000000−2i2i2i−2i0000000000
χ554-44-44-444-4-4-20022-2000-22-22-22000022−2222−2200−22−22−22−2200000000000000000000000000
χ564-44-44-444-4-4-20022-2000-22-22-220000−2222−2222002−22−22−22−200000000000000000000000000
χ574-44-44-4-4-444400-4-440004-4-44-4400000000000000000000000000000000000000000000
χ584-44-44-4-4-444-20022-2000-222-22-20000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ594-44-44-4-4-444-20022-2000-222-22-20000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ604-44-4-444-44-4-20022-20002-2-222-2000022−22−222200−222−2−222−200000000000000000000000000
χ614-44-4-444-44-4-20022-20002-2-222-20000−222222−22002−2−222−2−2200000000000000000000000000
χ624-44-4-44-44-44400-4-44000-44-444-400000000000000000000000000000000000000000000
χ634-44-4-44-44-44-20022-20002-22-2-220000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ644-44-4-44-44-44-20022-20002-22-2-220000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6588-8-8000000-48-84-4400000000000-440000000000000000000000000000000000000000
χ6688-8-8000000-4-884-44000000000004-40000000000000000000000000000000000000000
χ678-8-880000008008-8-800000000000000000000000000000000000000000000000000000
χ688-8-88000000-400-44400000000043−43000000000000000000000000000000000000000000
χ698-8-88000000-400-444000000000−4343000000000000000000000000000000000000000000

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