Finite Group Databasebeta

← Group #10853231

Character table — Group #10853231

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121216161616161616161616242424242424242424242424
order1222222234444666666622441212121244446688881212242424242424242444444444441212121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ61111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111
χ911111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-1-11111-1-1111-111-1-111-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111111-1-1-11111-1-1-1-1-11-1-111-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1-1-11111111-1-1-111-1-111
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-11-1-1-1-11111-1-1-1111-1-111-1-1
χ1311111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111-1-11111-1111-1-1-1-111-1-11-1-1-11111-1-1
χ1411111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-11111-1111-1-1-1-111
χ1511111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111111-11111-1-1-1-1-1-11-111-1-1-1-111
χ1611111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11-11111-1-1-1-111-11-1-11111-1-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-20000000022-2-20000000000000000-2200000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-200000000-2-22200000000000000002-200000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-20000220000000022220000000000000000-2-200000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-200002200000000-2-2-2-200000000000000002200000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-2-2-2-2-1-11111111100000000-2-2-1-111-1-111000000000000
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
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-111111111000000002211-1-111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21122-2-211-1-1-1-11111000000002-211-1-1-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-211-2-222111111-1-1-1-100000000-221111-1-1-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2221122-2-211-1-1-1-1111100000000-22-1-11111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211-2-222111111-1-1-1-1000000002-2-1-1-1-11111000000000000
χ29222-2-2-22-222-2-222-2-22-2-2200002-2-22000000002-200000022-2-200002i2i−2i−2i000000000000002i−2i000000
χ30222-2-2-22-222-2-222-2-22-2-2200002-2-22000000002-200000022-2-20000−2i−2i2i2i00000000000000−2i2i000000
χ31222-2-2-22-222-2-222-2-22-2-2200002-2-2200000000-22000000-2-22200002i2i−2i−2i00000000000000−2i2i000000
χ32222-2-2-22-222-2-222-2-22-2-2200002-2-2200000000-22000000-2-2220000−2i−2i2i2i000000000000002i−2i000000
χ3322-22-2-2-2222-22-2-2-2-2222-2000022-2-20000002i−2i00002i2i−2i−2i000000002i−2i2i−2i00000000000000002-20000
χ3422-22-2-2-2222-22-2-2-2-2222-2000022-2-20000002i−2i00002i2i−2i−2i00000000−2i2i−2i2i0000000000000000-220000
χ3522-22-2-2-2222-22-2-2-2-2222-2000022-2-2000000−2i2i0000−2i−2i2i2i000000002i−2i2i−2i0000000000000000-220000
χ3622-22-2-2-2222-22-2-2-2-2222-2000022-2-2000000−2i2i0000−2i−2i2i2i00000000−2i2i−2i2i00000000000000002-20000
χ3722-2-222-2-2222-2-2-2222-2-2-22-22-22-22-200002-200002-20000000000002-2-2200000000002-20000000000
χ3822-2-222-2-2222-2-2-2222-2-2-22-22-22-22-200002-200002-2000000000000-222-20000000000-220000000000
χ3922-2-222-2-2222-2-2-2222-2-2-2-22-222-22-20000-220000-220000000000002-2-220000000000-220000000000
χ4022-2-222-2-2222-2-2-2222-2-2-2-22-222-22-20000-220000-22000000000000-222-200000000002-20000000000
χ4122-2-222-2-22-2-222-2222-2-2-22-2-22-22-222i−2i2i−2i2-20000-220000000000000000002i−2i002i−2i00000000000000
χ4222-2-222-2-22-2-222-2222-2-2-22-2-22-22-22−2i2i−2i2i2-20000-22000000000000000000−2i2i00−2i2i00000000000000
χ4322-2-222-2-22-2-222-2222-2-2-2-222-2-22-222i−2i−2i2i-2200002-2000000000000000000−2i2i002i−2i00000000000000
χ4422-2-222-2-22-2-222-2222-2-2-2-222-2-22-22−2i2i2i−2i-2200002-20000000000000000002i−2i00−2i2i00000000000000
χ4522-2-222-2-2-1-2-2221-1-1-11112-2-221-11-12i−2i2i−2i-1100001-1−i3i3−i3i3−i3i3−i3i30000000000−ii3−3−ii3−3000000000000
χ4622-2-222-2-2-1-2-2221-1-1-11112-2-221-11-12i−2i2i−2i-1100001-1i3−i3i3−i3i3−i3i3−i30000000000−ii−33−ii−33000000000000
χ4722-2-222-2-2-1-2-2221-1-1-11112-2-221-11-1−2i2i−2i2i-1100001-1−i3i3−i3i3−i3i3−i3i30000000000i−i−33i−i−33000000000000
χ4822-2-222-2-2-1-2-2221-1-1-11112-2-221-11-1−2i2i−2i2i-1100001-1i3−i3i3−i3i3−i3i3−i30000000000i−i3−3i−i3−3000000000000
χ4922-2-222-2-2-1-2-2221-1-1-1111-222-21-11-12i−2i−2i2i1-10000-11−i3i3−i3i3i3−i3i3−i30000000000i−i3−3−ii−33000000000000
χ5022-2-222-2-2-1-2-2221-1-1-1111-222-21-11-12i−2i−2i2i1-10000-11i3−i3i3−i3−i3i3−i3i30000000000i−i−33−ii3−3000000000000
χ5122-2-222-2-2-1-2-2221-1-1-1111-222-21-11-1−2i2i2i−2i1-10000-11−i3i3−i3i3i3−i3i3−i30000000000−ii−33i−i3−3000000000000
χ5222-2-222-2-2-1-2-2221-1-1-1111-222-21-11-1−2i2i2i−2i1-10000-11i3−i3i3−i3−i3i3−i3i30000000000−ii3−3i−i−33000000000000
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
χ55444-4-4-44-44-444-44-4-44-4-440000-444-400000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-24-4-44-222-222-20000-222-2000000004-4000000-2-222000000000000000000000000000000
χ57444-4-4-44-4-24-4-44-222-222-20000-222-200000000-4400000022-2-2000000000000000000000000000000
χ58444-4-4-44-4-2-444-4-222-222-200002-2-2200000000000023−23−23230000000000000000000000000000000000
χ59444-4-4-44-4-2-444-4-222-222-200002-2-22000000000000−232323−230000000000000000000000000000000000
χ6044-44-4-4-444-44-44-4-4-4444-40000-4-44400000000000000000000000000000000000000000000000000
χ6144-44-4-4-44-24-44-4222-2-2-220000-2-2220000004i−4i0000−2i−2i2i2i0000000000000000000000000000000000
χ6244-44-4-4-44-24-44-4222-2-2-220000-2-222000000−4i4i00002i2i−2i−2i0000000000000000000000000000000000
χ6344-44-4-4-44-2-44-44222-2-2-22000022-2-20000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6444-44-4-4-44-2-44-44222-2-2-22000022-2-200000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ6544-4-444-4-4-244-4-42-2-2-22224-44-4-22-220000-220000-2200000000000000000000000000000000000000
χ6644-4-444-4-4-244-4-42-2-2-2222-44-44-22-2200002-200002-200000000000000000000000000000000000000
χ674-4444-4-4-44000044-4-44-4-400000000000000000000000000000000000000000000000000000022−2200
χ684-4444-4-4-44000044-4-44-4-4000000000000000000000000000000000000000000000000000000−222200
χ694-44-4-44-44400004-44-4-44-40000000000000000000000000000004i−4i00000000000000000000000000
χ704-44-4-44-44400004-44-4-44-4000000000000000000000000000000−4i4i00000000000000000000000000
χ714-4-44-444-440000-4-44-44-4400000000000000000000000000004i−4i0000000000000000000000000000
χ724-4-44-444-440000-4-44-44-440000000000000000000000000000−4i4i0000000000000000000000000000
χ734-4-4-44-44440000-44-4-4-4440000000000000000000000000000000000000000000000000000000022−22
χ744-4-4-44-44440000-44-4-4-44400000000000000000000000000000000000000000000000000000000−2222
χ758-8888-8-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000
χ768-88-8-88-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000
χ778-8-88-888-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-88-888-400004-4444-4-40000000000000000000000000000000000000000000000000000000000

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