Finite Group Databasebeta

← Group #10855138

Character table — Group #10855138

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order1222222234444666666622441212121212121212444444446688881212121212121212242424242424242444444444121212122444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ911111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11-11111-1-1-11
χ1011111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-11-1-1-1-1111-1
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11-111-1-1111-1
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-11-1-111-1-1-11
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11111-1-1111-1-1-1-1-111-11
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-111111-1-11-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1111-1-1-111-1-11-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-111-11
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002200000000000000000000222200000000-2-200000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002200000000000000000000-2-2-2-2000000002200000000
χ19222222222-2-2-2-22222222-2-222-2-22222-2-200000000-2-20000000000000000000022-2-200000000-2200000000
χ20222222222-2-2-2-22222222-2-222-2-22222-2-200000000-2-200000000000000000000-2-222000000002-200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-2-2-2-2111111111111111100000000-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-222-2-21122-2-21111-1-1-1-1-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-2-2-22211-2-222-1-1-1-111111111-1-1-1-100000000-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-22222-2-211-2-2221111-1-1-1-11111-1-1-1-10000000011-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-222-2-2221122-2-2-1-1-1-11111-1-1-1-111110000000011-1-10000000000
χ29222-2-22-2-22-22-222-2-222-2-200002-200002-200002i−2i0000000000002i2i−2i−2i0000000000002i2i−2i−2i00000000002-200
χ30222-2-22-2-22-22-222-2-222-2-200002-200002-200002i−2i0000000000002i2i−2i−2i000000000000−2i−2i2i2i0000000000-2200
χ31222-2-22-2-22-22-222-2-222-2-200002-200002-20000−2i2i000000000000−2i−2i2i2i0000000000002i2i−2i−2i0000000000-2200
χ32222-2-22-2-22-22-222-2-222-2-200002-200002-20000−2i2i000000000000−2i−2i2i2i000000000000−2i−2i2i2i00000000002-200
χ332-2-22-222-222-2-22-2222-2-2-22-22-22222-2-2-2-2000000002-20000000000000000000000002i−2i2i−2i0000002i−2i000000
χ342-2-22-222-222-2-22-2222-2-2-22-22-22222-2-2-2-2000000002-2000000000000000000000000−2i2i−2i2i000000−2i2i000000
χ352-2-22-222-222-2-22-2222-2-2-2-22-2222-2-222-2-200000000-220000000000000000000000002i−2i2i−2i000000−2i2i000000
χ362-2-22-222-222-2-22-2222-2-2-2-22-2222-2-222-2-200000000-22000000000000000000000000−2i2i−2i2i0000002i−2i000000
χ372-2-22-222-22-222-2-2222-2-2-22-2-22-2-2-2-222222i−2i2i−2i00002-200000000000000000000000000002i−2i2i−2i0000000000
χ382-2-22-222-22-222-2-2222-2-2-22-2-22-2-2-2-22222−2i2i−2i2i00002-20000000000000000000000000000−2i2i−2i2i0000000000
χ392-2-22-222-22-222-2-2222-2-2-2-222-2-2-222-2-2222i−2i−2i2i0000-2200000000000000000000000000002i−2i−2i2i0000000000
χ402-2-22-222-22-222-2-2222-2-2-2-222-2-2-222-2-222−2i2i2i−2i0000-220000000000000000000000000000−2i2i2i−2i0000000000
χ412-2-22-222-2-1-222-21-1-1-11112-2-221111-1-1-1-12i−2i2i−2i0000-11000033−3−33−33−3−i3−i3i3i3−i3−i3i3i300000000−ii−ii0000000000
χ422-2-22-222-2-1-222-21-1-1-11112-2-221111-1-1-1-12i−2i2i−2i0000-110000−3−333−33−33i3i3−i3−i3i3i3−i3−i300000000−ii−ii0000000000
χ432-2-22-222-2-1-222-21-1-1-11112-2-221111-1-1-1-1−2i2i−2i2i0000-11000033−3−33−33−3i3i3−i3−i3i3i3−i3−i300000000i−ii−i0000000000
χ442-2-22-222-2-1-222-21-1-1-11112-2-221111-1-1-1-1−2i2i−2i2i0000-110000−3−333−33−33−i3−i3i3i3−i3−i3i3i300000000i−ii−i0000000000
χ452-2-22-222-2-1-222-21-1-1-1111-222-211-1-111-1-12i−2i−2i2i00001-1000033−3−3−33−33i3i3−i3−i3−i3−i3i3i300000000−iii−i0000000000
χ462-2-22-222-2-1-222-21-1-1-1111-222-211-1-111-1-12i−2i−2i2i00001-10000−3−3333−33−3−i3−i3i3i3i3i3−i3−i300000000−iii−i0000000000
χ472-2-22-222-2-1-222-21-1-1-1111-222-211-1-111-1-1−2i2i2i−2i00001-1000033−3−3−33−33−i3−i3i3i3i3i3−i3−i300000000i−i−ii0000000000
χ482-2-22-222-2-1-222-21-1-1-1111-222-211-1-111-1-1−2i2i2i−2i00001-10000−3−3333−33−3i3i3−i3−i3−i3−i3i3i300000000i−i−ii0000000000
χ492-2-2-222-222-2-222-2-2-22-22200002-20000-220000002-20000002-22-200000000000000002-2-22000000002-20000
χ502-2-2-222-222-2-222-2-2-22-22200002-20000-220000002-20000002-22-20000000000000000-222-200000000-220000
χ512-2-2-222-222-2-222-2-2-22-22200002-20000-22000000-22000000-22-2200000000000000002-2-2200000000-220000
χ522-2-2-222-222-2-222-2-2-22-22200002-20000-22000000-22000000-22-220000000000000000-222-2000000002-20000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-42222222200000000-2-2000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422-2-2-2-2220000000022000000000000000000000000000000000000000000
χ55444-4-44-4-444-44-44-4-444-4-40000-440000-440000000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-24-44-4-222-2-22200002-200002-20000000000000023−23−23230000000000000000000000000000000000
χ57444-4-44-4-4-24-44-4-222-2-22200002-200002-200000000000000−232323−230000000000000000000000000000000000
χ58444-4-44-4-4-2-44-44-222-2-2220000-220000-2200004i−4i000000000000−2i−2i2i2i000000000000000000000000000000
χ59444-4-44-4-4-2-44-44-222-2-2220000-220000-220000−4i4i0000000000002i2i−2i−2i000000000000000000000000000000
χ6044-44-4-4-444000044-4-4-44-4000000000000000000000000000000000000000000004i−4i000000000000000000
χ6144-44-4-4-444000044-4-4-44-400000000000000000000000000000000000000000000−4i4i000000000000000000
χ6244-4-44-44-4400004-44-4-4-440000000000000000000000−2i22i20000000000−2i22i2−2i22i200000000000000000000000000
χ6344-4-44-44-4400004-44-4-4-4400000000000000000000002i2−2i200000000002i2−2i22i2−2i200000000000000000000000000
χ6444-4-44-44-4-20000-22-2222-200000023−2323−23000000000000−2i22i20000000000i2−i2i2−i2i6−i6i6−i60000000000000000000000
χ6544-4-44-44-4-20000-22-2222-200000023−2323−230000000000002i2−2i20000000000−i2i2−i2i2−i6i6−i6i60000000000000000000000
χ6644-4-44-44-4-20000-22-2222-2000000−2323−2323000000000000−2i22i20000000000i2−i2i2−i2−i6i6−i6i60000000000000000000000
χ6744-4-44-44-4-20000-22-2222-2000000−2323−23230000000000002i2−2i20000000000−i2i2−i2i2i6−i6i6−i60000000000000000000000
χ684-4444-4-4-440000-44-4-44-440000000000000000000000000000000000000000004i−4i00000000000000000000
χ694-4444-4-4-440000-44-4-44-44000000000000000000000000000000000000000000−4i4i00000000000000000000
χ704-44-4-4-44440000-4-44-444-400000000000000000000000022−2200000000000022−22−22220000000000000000000000
χ714-44-4-4-44440000-4-44-444-4000000000000000000000000−2222000000000000−222222−220000000000000000000000
χ724-44-4-4-444-2000022-22-2-2200000023−23−23230000000000000022−2200000000−666−6−222−20000000000000000000000
χ734-44-4-4-444-2000022-22-2-2200000023−23−232300000000000000−2222000000006−6−662−2−220000000000000000000000
χ744-44-4-4-444-2000022-22-2-22000000−232323−230000000000000022−22000000006−6−66−222−20000000000000000000000
χ754-44-4-4-444-2000022-22-2-22000000−232323−2300000000000000−222200000000−666−62−2−220000000000000000000000
χ764-4-44-444-4-24-4-442-2-2-22224-44-4-2-2-2-2222200000000-22000000000000000000000000000000000000000000
χ774-4-44-444-4-24-4-442-2-2-2222-44-44-2-222-2-222000000002-2000000000000000000000000000000000000000000
χ784-4-4-444-44444-4-4-4-4-44-4440000-4400004-40000000000000000000000000000000000000000000000000000
χ794-4-4-444-44-244-4-4222-22-2-200002-20000-22000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ804-4-4-444-44-244-4-4222-22-2-200002-20000-220000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ814-4-4-444-44-2-4-444222-22-2-20000-2200002-20000004-4000000-22-220000000000000000000000000000000000
χ824-4-4-444-44-2-4-444222-22-2-20000-2200002-2000000-440000002-22-20000000000000000000000000000000000
χ8388-88-8-8-88-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8888-8-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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