Finite Group Databasebeta

← Group #10855140

Character table — Group #10855140

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121216161616161616161616242424242424242424242424
order12222222344446666666224412121212444466888812122424242424242424444444442466121212121212244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111
χ911111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111111-11111-1-1-1-1-1111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-11111-1-1-1-11-1-1-11111-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-11-1-111-1-111-11-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-1-1111-11111-1-111-1-1
χ1311111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11-1-1-1-11111-11-1-1111111-1-1
χ1411111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-11-1-1-1-111111-111-1-1-1-1-1-111
χ1511111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11-111-1-111-1-1-111111-1-1-1-111
χ1611111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111111-111-1-111-1-11-1-1-1-1-11111-1-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-200000000222200000000000000-2-20000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-200000000-2-2-2-200000000000000220000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-20000220000000022-2-2000000000000002-20000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-200002200000000-2-22200000000000000-220000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-2-2-2-2-1-11111111100000000-2-211-1-1-1-111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-211111111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-1111111110000000022-1-11111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21122-2-211-1-1-1-11111000000002-2-1-1-1-11111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-211-2-222111111-1-1-1-100000000-2211-1-111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2221122-2-211-1-1-1-1111100000000-221111-1-1-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211-2-222111111-1-1-1-1000000002-2-1-111-1-111000000000000
χ29222-22-2-2-22-222-22-2-222-2-200002-2-220000002-2000022-2-2000000002i2i−2i−2i0000000000002i−2i00000000
χ30222-22-2-2-22-222-22-2-222-2-200002-2-220000002-2000022-2-200000000−2i−2i2i2i000000000000−2i2i00000000
χ31222-22-2-2-22-222-22-2-222-2-200002-2-22000000-220000-2-222000000002i2i−2i−2i000000000000−2i2i00000000
χ32222-22-2-2-22-222-22-2-222-2-200002-2-22000000-220000-2-22200000000−2i−2i2i2i0000000000002i−2i00000000
χ332-2-2222-2-2222-2-2-22-22-22-22-22-2-22-2200002-200002-20000000000002i−2i2i−2i000000000000002i−2i000000
χ342-2-2222-2-2222-2-2-22-22-22-22-22-2-22-2200002-200002-2000000000000−2i2i−2i2i00000000000000−2i2i000000
χ352-2-2222-2-2222-2-2-22-22-22-2-22-22-22-220000-220000-220000000000002i−2i2i−2i00000000000000−2i2i000000
χ362-2-2222-2-2222-2-2-22-22-22-2-22-22-22-220000-220000-22000000000000−2i2i−2i2i000000000000002i−2i000000
χ372-2-2222-2-22-2-222-22-22-22-22-2-222-22-22i−2i2i−2i2-20000-22000000000000000000002i−2i2i−2i00000000000000
χ382-2-2222-2-22-2-222-22-22-22-22-2-222-22-2−2i2i−2i2i2-20000-2200000000000000000000−2i2i−2i2i00000000000000
χ392-2-2222-2-22-2-222-22-22-22-2-222-22-22-22i−2i−2i2i-2200002-2000000000000000000002i−2i−2i2i00000000000000
χ402-2-2222-2-22-2-222-22-22-22-2-222-22-22-2−2i2i2i−2i-2200002-200000000000000000000−2i2i2i−2i00000000000000
χ412-2-2222-2-2-1-2-2221-11-11-112-2-22-11-112i−2i2i−2i-1100001-13−33−333−3−30000000000−i3i3−ii−ii−i3i3000000000000
χ422-2-2222-2-2-1-2-2221-11-11-112-2-22-11-112i−2i2i−2i-1100001-1−33−33−3−3330000000000i3−i3−ii−iii3−i3000000000000
χ432-2-2222-2-2-1-2-2221-11-11-112-2-22-11-11−2i2i−2i2i-1100001-13−33−333−3−30000000000i3−i3i−ii−ii3−i3000000000000
χ442-2-2222-2-2-1-2-2221-11-11-112-2-22-11-11−2i2i−2i2i-1100001-1−33−33−3−3330000000000−i3i3i−ii−i−i3i3000000000000
χ452-2-2222-2-2-1-2-2221-11-11-11-222-2-11-112i−2i−2i2i1-10000-113−33−3−3−3330000000000−i3i3−iii−ii3−i3000000000000
χ462-2-2222-2-2-1-2-2221-11-11-11-222-2-11-112i−2i−2i2i1-10000-11−33−3333−3−30000000000i3−i3−iii−i−i3i3000000000000
χ472-2-2222-2-2-1-2-2221-11-11-11-222-2-11-11−2i2i2i−2i1-10000-113−33−3−3−3330000000000i3−i3i−i−ii−i3i3000000000000
χ482-2-2222-2-2-1-2-2221-11-11-11-222-2-11-11−2i2i2i−2i1-10000-11−33−3333−3−30000000000−i3i3i−i−iii3−i3000000000000
χ492-2-2-22-2222-22-22-2-222-2-220000-2-222000000002-20000002-22-200002-2-2200000000000000002-20000
χ502-2-2-22-2222-22-22-2-222-2-220000-2-222000000002-20000002-22-20000-222-20000000000000000-220000
χ512-2-2-22-2222-22-22-2-222-2-220000-2-22200000000-22000000-22-2200002-2-220000000000000000-220000
χ522-2-2-22-2222-22-22-2-222-2-220000-2-22200000000-22000000-22-220000-222-200000000000000002-20000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422220000-2-200002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000220000-2-200000000000000000000000000000000000000
χ55444-44-4-4-444-4-444-4-444-4-40000-444-400000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-24-4-44-222-2-22200002-2-22000000000000000023−23−2323000000000000000000000000000000
χ57444-44-4-4-4-24-4-44-222-2-22200002-2-220000000000000000−232323−23000000000000000000000000000000
χ58444-44-4-4-4-2-444-4-222-2-2220000-222-20000004-40000-2-2220000000000000000000000000000000000
χ59444-44-4-4-4-2-444-4-222-2-2220000-222-2000000-44000022-2-20000000000000000000000000000000000
χ6044-44-4-4-4440000444-4-4-4-400000000000000000000000000004i−4i0000000000000000000000000000
χ6144-44-4-4-4440000444-4-4-4-40000000000000000000000000000−4i4i0000000000000000000000000000
χ6244-4-4-444-4400004-4-4-4-444000000000000000000000000000000000000000000000000000000−2i22i200
χ6344-4-4-444-4400004-4-4-4-4440000000000000000000000000000000000000000000000000000002i2−2i200
χ644-444-4-44-440000-44-4-44-440000000000000000000000000000004i−4i00000000000000000000000000
χ654-444-4-44-440000-44-4-44-44000000000000000000000000000000−4i4i00000000000000000000000000
χ664-44-4-44-4440000-4-44-444-40000000000000000000000000000000000000000000000000000000022−22
χ674-44-4-44-4440000-4-44-444-400000000000000000000000000000000000000000000000000000000−2222
χ684-4-4444-4-4-244-4-42-22-22-224-44-42-22-20000-220000-2200000000000000000000000000000000000000
χ694-4-4444-4-4-244-4-42-22-22-22-44-442-22-200002-200002-200000000000000000000000000000000000000
χ704-4-4-44-44444-44-4-4-444-4-44000044-4-400000000000000000000000000000000000000000000000000
χ714-4-4-44-444-24-44-422-2-222-20000-2-22200000000000023−23−23230000000000000000000000000000000000
χ724-4-4-44-444-24-44-422-2-222-20000-2-222000000000000−232323−230000000000000000000000000000000000
χ734-4-4-44-444-2-44-4422-2-222-2000022-2-2000000004-4000000-22-22000000000000000000000000000000
χ744-4-4-44-444-2-44-4422-2-222-2000022-2-200000000-440000002-22-2000000000000000000000000000000
χ7588-88-8-8-88-40000-4-4-444440000000000000000000000000000000000000000000000000000000000
χ7688-8-8-888-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000
χ778-888-8-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000
χ788-88-8-88-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000

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