Finite Group Databasebeta

← Group #10853229

Character table — Group #10853229

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order12222222344446666666224466661212121244444444888812121212121212121212242424242424242444444444121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1111111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1111-1-1-11
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1111-1
χ1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-11-1-111-11
χ1211111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11-111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-11-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111111-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-111-1111-1-11-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-11
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-20000000000000000220000-2-20000002-2000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-20000000000000000-2-2000022000000-22000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000022000000000000000022000022000000-2-2000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-20000-2-200000022000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1111111111111111100000000-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-111110000000011-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-100000000-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-10000000011-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-1111100000000-1-1110000000000
χ29222-2-2-2-2222-2-222-2-2-222-2000000002-22-2002i−2i000000000000002i2i−2i−2i00000000002i2i−2i−2i0000000000002-200
χ30222-2-2-2-2222-2-222-2-2-222-2000000002-22-2002i−2i000000000000002i2i−2i−2i0000000000−2i−2i2i2i000000000000-2200
χ31222-2-2-2-2222-2-222-2-2-222-2000000002-22-200−2i2i00000000000000−2i−2i2i2i00000000002i2i−2i−2i000000000000-2200
χ32222-2-2-2-2222-2-222-2-2-222-2000000002-22-200−2i2i00000000000000−2i−2i2i2i0000000000−2i−2i2i2i0000000000002-200
χ3322-222-2-2-2222-2-2-222-22-2-22-22-222-2-222-2-20000000000002-20000000000000000002-22-20000002-200000000
χ3422-222-2-2-2222-2-2-222-22-2-22-22-222-2-222-2-20000000000002-2000000000000000000-22-22000000-2200000000
χ3522-222-2-2-2222-2-2-222-22-2-2-22-22-2-22222-2-2000000000000-220000000000000000002-22-2000000-2200000000
χ3622-222-2-2-2222-2-2-222-22-2-2-22-22-2-22222-2-2000000000000-22000000000000000000-22-220000002-200000000
χ3722-222-2-2-22-2-222-222-22-2-22-2-2222-2-2-2-22200002i−2i2i−2i0000-220000000000000000000000002i−2i2i−2i0000000000
χ3822-222-2-2-22-2-222-222-22-2-22-2-2222-2-2-2-2220000−2i2i−2i2i0000-22000000000000000000000000−2i2i−2i2i0000000000
χ3922-222-2-2-22-2-222-222-22-2-2-222-2-2-222-2-22200002i−2i−2i2i00002-2000000000000000000000000−2i2i2i−2i0000000000
χ4022-222-2-2-22-2-222-222-22-2-2-222-2-2-222-2-2220000−2i2i2i−2i00002-20000000000000000000000002i−2i−2i2i0000000000
χ4122-222-2-2-2-1-2-2221-1-11-1112-2-22-1-11111-1-100002i−2i2i−2i00001-133−3−33−33−3−i3−i3i3i3−i3−i3i3i300000000−ii−ii0000000000
χ4222-222-2-2-2-1-2-2221-1-11-1112-2-22-1-11111-1-100002i−2i2i−2i00001-1−3−333−33−33i3i3−i3−i3i3i3−i3−i300000000−ii−ii0000000000
χ4322-222-2-2-2-1-2-2221-1-11-1112-2-22-1-11111-1-10000−2i2i−2i2i00001-133−3−33−33−3i3i3−i3−i3i3i3−i3−i300000000i−ii−i0000000000
χ4422-222-2-2-2-1-2-2221-1-11-1112-2-22-1-11111-1-10000−2i2i−2i2i00001-1−3−333−33−33−i3−i3i3i3−i3−i3i3i300000000i−ii−i0000000000
χ4522-222-2-2-2-1-2-2221-1-11-111-222-211-1-111-1-100002i−2i−2i2i0000-1133−3−3−33−33−i3−i3i3i3i3i3−i3−i300000000i−i−ii0000000000
χ4622-222-2-2-2-1-2-2221-1-11-111-222-211-1-111-1-100002i−2i−2i2i0000-11−3−3333−33−3i3i3−i3−i3−i3−i3i3i300000000i−i−ii0000000000
χ4722-222-2-2-2-1-2-2221-1-11-111-222-211-1-111-1-10000−2i2i2i−2i0000-1133−3−3−33−33i3i3−i3−i3−i3−i3i3i300000000−iii−i0000000000
χ4822-222-2-2-2-1-2-2221-1-11-111-222-211-1-111-1-10000−2i2i2i−2i0000-11−3−3333−33−3−i3−i3i3i3i3i3−i3−i300000000−iii−i0000000000
χ4922-2-2-222-222-22-2-2-2-222-22000000002-2-222-20000000000002-22-2000000000000002i−2i−2i2i00000000002i−2i0000
χ5022-2-2-222-222-22-2-2-2-222-22000000002-2-222-20000000000002-22-200000000000000−2i2i2i−2i0000000000−2i2i0000
χ5122-2-2-222-222-22-2-2-2-222-22000000002-2-22-22000000000000-22-22000000000000002i−2i−2i2i0000000000−2i2i0000
χ5222-2-2-222-222-22-2-2-2-222-22000000002-2-22-22000000000000-22-2200000000000000−2i2i2i−2i00000000002i−2i0000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-222220000000000002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422222222000000000000-2-200000000000000000000000000000000000000
χ55444-4-4-4-444-444-44-4-4-444-400000000-44-440000000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-24-4-44-2222-2-2200000000-22-22004i−4i00000000000000−2i−2i2i2i000000000000000000000000000000
χ57444-4-4-4-44-24-4-44-2222-2-2200000000-22-2200−4i4i000000000000002i2i−2i−2i000000000000000000000000000000
χ58444-4-4-4-44-2-444-4-2222-2-22000000002-22-20000000000000023−23−23230000000000000000000000000000000000
χ59444-4-4-4-44-2-444-4-2222-2-22000000002-22-200000000000000−232323−230000000000000000000000000000000000
χ6044-444-4-4-4-244-4-42-2-22-2224-44-4-2-222-2-222000000000000-2200000000000000000000000000000000000000
χ6144-444-4-4-4-244-4-42-2-22-222-44-4422-2-2-2-2220000000000002-200000000000000000000000000000000000000
χ6244-4-4-444-44-44-44-4-4-444-4400000000-444-40000000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-24-44-4222-2-22-200000000-222-24-4000000000000-22-220000000000000000000000000000000000
χ6444-4-4-444-4-24-44-4222-2-22-200000000-222-2-440000000000002-22-20000000000000000000000000000000000
χ6544-4-4-444-4-2-44-44222-2-22-2000000002-2-22000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6644-4-4-444-4-2-44-44222-2-22-2000000002-2-220000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ674-444-44-4-44000044-44-4-4-40000000000000000000022−2200000000000022−2222−2200000000000000000000000000
χ684-444-44-4-44000044-44-4-4-400000000000000000000−2222000000000000−2222−222200000000000000000000000000
χ694-444-44-4-4-20000-2-22-22220000−2i32i3−2i32i300000000000022−22000000000000−22−22i6−i6i6−i60000000000000000000000
χ704-444-44-4-4-20000-2-22-22220000−2i32i3−2i32i3000000000000−22220000000000002−22−2−i6i6−i6i60000000000000000000000
χ714-444-44-4-4-20000-2-22-222200002i3−2i32i3−2i300000000000022−22000000000000−22−22−i6i6−i6i60000000000000000000000
χ724-444-44-4-4-20000-2-22-222200002i3−2i32i3−2i3000000000000−22220000000000002−22−2i6−i6i6−i60000000000000000000000
χ734-44-44-44-4400004-44-4-4-440000000000000000000000000000000000000000000000004i−4i00000000000000
χ744-44-44-44-4400004-44-4-4-44000000000000000000000000000000000000000000000000−4i4i00000000000000
χ754-4-44-4-44440000-44-4-4-444000000000000000000000022−220000000000000022−22−22220000000000000000000000
χ764-4-44-4-44440000-44-4-4-4440000000000000000000000−222200000000000000−222222−220000000000000000000000
χ774-4-44-4-444-200002-2222-2-20000−2i32i32i3−2i30000000000000022−220000000000i6−i6−i6i6−222−20000000000000000000000
χ784-4-44-4-444-200002-2222-2-20000−2i32i32i3−2i300000000000000−22220000000000−i6i6i6−i62−2−220000000000000000000000
χ794-4-44-4-444-200002-2222-2-200002i3−2i3−2i32i30000000000000022−220000000000−i6i6i6−i6−222−20000000000000000000000
χ804-4-44-4-444-200002-2222-2-200002i3−2i3−2i32i300000000000000−22220000000000i6−i6−i6i62−2−220000000000000000000000
χ814-4-4-444-4440000-4-444-44-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ824-4-4-444-4440000-4-444-44-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ838-88-88-88-8-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-4000044-4-44-440000000000000000000000000000000000000000000000000000000000000000

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