Finite Group Databasebeta

← Group #10697947

Character table — Group #10697947

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488881212121212121212161616161616161616161616161616161616484848484848
order1222344444466624441212121212126121212444444442444668812121212121224242424448888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-11-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111
χ92222222-222-2222-2-2-22222-2-22-2-2-220000000020-20220000-2-2000000000000
χ102222222-222-2222-2-2-22222-2-22-2-2-2200000000-2020-2-2000022000000000000
χ11222222-222-22222-2-22-2-2-22222-22-2-200000000020-200002200-2-20000000000
χ12222222-222-22222-2-22-2-2-22222-22-2-2000000000-2020000-2-200220000000000
χ13222222-2-22-2-222222-2-2-2-22-2-222-22-2000000000000002-200000022-2-2000000
χ14222222-2-22-2-222222-2-2-2-22-2-222-22-200000000000000-22000000-2-222000000
χ1522222-222-222222-22-2-222-222-2-2-22-2000000000000000000000000002-20000
χ1622222-222-222222-22-2-222-222-2-2-22-200000000000000000000000000-220000
χ1722222-22-2-22-22222-22-222-2-2-2-222-2-20000000000000000000000000000002-2
χ1822222-22-2-22-22222-22-222-2-2-2-222-2-2000000000000000000000000000000-22
χ1922222-2-22-2-222222-2-22-2-2-222-22-2-2200000000000000000000000000002-200
χ2022222-2-22-2-222222-2-22-2-2-222-22-2-220000000000000000000000000000-2200
χ2122222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ2222222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-122-1-1-1-1-1-1-1-1-1-1000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002-22-2-1-1-2-211-1-1111111000000
χ252222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-22-2211-2-2-1-111-1-11111000000
χ262222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21122111111-1-1-1-1000000
χ272222-122-222-2-1-1-1-2-2-22-1-1-111-1111-10000000020-20-1-100−i3i311−i3i3−i3i3−i3i3000000
χ282222-122-222-2-1-1-1-2-2-22-1-1-111-1111-10000000020-20-1-100i3−i311i3−i3i3−i3i3−i3000000
χ292222-122-222-2-1-1-1-2-2-22-1-1-111-1111-100000000-20201100−i3i3-1-1−i3i3i3−i3i3−i3000000
χ302222-122-222-2-1-1-1-2-2-22-1-1-111-1111-100000000-20201100i3−i3-1-1i3−i3−i3i3−i3i3000000
χ312222-12-222-22-1-1-1-2-22-211-1-1-1-11-11100000000020-2−i3i300-1-1−i3i311−i3i3i3−i3000000
χ322222-12-222-22-1-1-1-2-22-211-1-1-1-11-11100000000020-2i3−i300-1-1i3−i311i3−i3−i3i3000000
χ332222-12-222-22-1-1-1-2-22-211-1-1-1-11-111000000000-202−i3i30011−i3i3-1-1i3−i3−i3i3000000
χ342222-12-222-22-1-1-1-2-22-211-1-1-1-11-111000000000-202i3−i30011i3−i3-1-1−i3i3i3−i3000000
χ352222-12-2-22-2-2-1-1-122-2-211-111-1-11-11000000000000−i3i32-2−i3i3i3−i3i3−i3-1-111000000
χ362222-12-2-22-2-2-1-1-122-2-211-111-1-11-11000000000000−i3i3-22i3−i3i3−i3−i3i311-1-1000000
χ372222-12-2-22-2-2-1-1-122-2-211-111-1-11-11000000000000i3−i32-2i3−i3−i3i3−i3i3-1-111000000
χ382222-12-2-22-2-2-1-1-122-2-211-111-1-11-11000000000000i3−i3-22−i3i3−i3i3i3−i311-1-1000000
χ394444-2-444-444-2-2-2-44-4-4-2-22-2-2222-2200000000000000000000000000000000
χ404444-2-44-4-44-4-2-2-24-44-4-2-22222-2-22200000000000000000000000000000000
χ414444-2-4-44-4-44-2-2-24-4-44222-2-22-222-200000000000000000000000000000000
χ424444-2-4-4-4-4-4-4-2-2-2-44442222222-2-2-200000000000000000000000000000000
χ4344-4-44400-400-44-4000000400-4000022-2-222-2-2000000000000000000000000
χ4444-4-44400-400-44-4000000400-40000-2-222-2-222000000000000000000000000
χ4544-4-44-400400-44-4000000-400400002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4644-4-44-400400-44-4000000-40040000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ474-44-440400-404-4-400004-4000000002-22-22-22-2000000000000000000000000
χ484-44-440400-404-4-400004-400000000-22-22-22-22000000000000000000000000
χ494-44-440-400404-4-40000-44000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ504-44-440-400404-4-40000-4400000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ514-4-44400400-4-4-4400000004-4000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ524-4-44400400-4-4-4400000004-400000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ534-4-44400-4004-4-440000000-44000002-2-222-2-22000000000000000000000000
χ544-4-44400-4004-4-440000000-4400000-222-2-222-2000000000000000000000000
χ5588-8-8-4800-8004-44000000-4004000000000000000000000000000000000000
χ5688-8-8-4-8008004-44000000400-4000000000000000000000000000000000000
χ578-88-8-40800-80-4440000-440000000000000000000000000000000000000000
χ588-88-8-40-80080-44400004-40000000000000000000000000000000000000000
χ598-8-88-400800-844-40000000-440000000000000000000000000000000000000
χ608-8-88-400-800844-400000004-40000000000000000000000000000000000000

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