Finite Group Databasebeta

← Group #10855121

Character table — Group #10855121

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121244668888121212121212121224242424242424244444441212121224444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111
χ911111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-1-1111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-11-1-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-11-1-1111-1-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111-11-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-1111-111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-11-1-11111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111-111-1-11-111-1-1-1-11111-1-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200220000000000000000000022-2-20000002-2000000000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2002200000000000000000000-2-222000000-22000000000000
χ19222222222-2-2-2-22222222-2-2220000-2-22222-2-200-2-2000000000000000000002222000000-2-2000000000000
χ20222222222-2-2-2-22222222-2-2220000-2-22222-2-200-2-200000000000000000000-2-2-2-200000022000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1222211111111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-21122-2-2-1-1-1-11111-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-211-2-222-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1221122-2-21111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-12211-2-2221111-1-1-1-11111-1-1-1-100002-2-1-11100000000000000
χ2922-2-222-2-22-22-2222-2-2-2-2200002i2i−2i−2i2-200002-2000000002i2i−2i−2i0000000000000000000000000000002i−2i002-2
χ3022-2-222-2-22-22-2222-2-2-2-2200002i2i−2i−2i2-200002-2000000002i2i−2i−2i000000000000000000000000000000−2i2i00-22
χ3122-2-222-2-22-22-2222-2-2-2-220000−2i−2i2i2i2-200002-200000000−2i−2i2i2i0000000000000000000000000000002i−2i00-22
χ3222-2-222-2-22-22-2222-2-2-2-220000−2i−2i2i2i2-200002-200000000−2i−2i2i2i000000000000000000000000000000−2i2i002-2
χ332-222-22-2-222-2-22-2-222-2-222-22-22i−2i2i−2i2222-2-2-2-22i−2i2-200002i−2i2i−2i2i2i−2i−2i00000000000000000000000000000000
χ342-222-22-2-222-2-22-2-222-2-222-22-2−2i2i−2i2i2222-2-2-2-2−2i2i2-20000−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000
χ352-222-22-2-222-2-22-2-222-2-22-22-222i−2i2i−2i22-2-222-2-2−2i2i-2200002i−2i2i−2i−2i−2i2i2i00000000000000000000000000000000
χ362-222-22-2-222-2-22-2-222-2-22-22-22−2i2i−2i2i22-2-222-2-22i−2i-220000−2i2i−2i2i2i2i−2i−2i00000000000000000000000000000000
χ372-222-22-2-22-222-2-2-222-2-222-2-220000-2-2-2-22222002-2000000000000000000000000000000002i−2i2i−2i00000000
χ382-222-22-2-22-222-2-2-222-2-222-2-220000-2-2-2-22222002-200000000000000000000000000000000−2i2i−2i2i00000000
χ392-222-22-2-22-222-2-2-222-2-22-222-20000-2-222-2-22200-22000000000000000000000000000000002i−2i−2i2i00000000
χ402-222-22-2-22-222-2-2-222-2-22-222-20000-2-222-2-22200-2200000000000000000000000000000000−2i2i2i−2i00000000
χ412-222-22-2-2-12-2-2211-1-111-12-22-22i−2i2i−2i-1-1-1-111112i−2i-110000−ii−ii−i−iii33−3−333−3−3000000−i3i3−i3i300000000000000
χ422-222-22-2-2-12-2-2211-1-111-12-22-22i−2i2i−2i-1-1-1-111112i−2i-110000−ii−ii−i−iii−3−333−3−333000000i3−i3i3−i300000000000000
χ432-222-22-2-2-12-2-2211-1-111-12-22-2−2i2i−2i2i-1-1-1-11111−2i2i-110000i−ii−iii−i−i33−3−333−3−3000000i3−i3i3−i300000000000000
χ442-222-22-2-2-12-2-2211-1-111-12-22-2−2i2i−2i2i-1-1-1-11111−2i2i-110000i−ii−iii−i−i−3−333−3−333000000−i3i3−i3i300000000000000
χ452-222-22-2-2-12-2-2211-1-111-1-22-222i−2i2i−2i-1-111-1-111−2i2i1-10000−ii−iiii−i−i33−3−3−3−333000000−i3i3i3−i300000000000000
χ462-222-22-2-2-12-2-2211-1-111-1-22-222i−2i2i−2i-1-111-1-111−2i2i1-10000−ii−iiii−i−i−3−33333−3−3000000i3−i3−i3i300000000000000
χ472-222-22-2-2-12-2-2211-1-111-1-22-22−2i2i−2i2i-1-111-1-1112i−2i1-10000i−ii−i−i−iii33−3−3−3−333000000i3−i3−i3i300000000000000
χ482-222-22-2-2-12-2-2211-1-111-1-22-22−2i2i−2i2i-1-111-1-1112i−2i1-10000i−ii−i−i−iii−3−33333−3−3000000−i3i3i3−i300000000000000
χ492-2-2-2-22222-2-222-2-2-2-222200002-2-222-20000-22000000002-2-2200000000000000000000000000002-2002-200
χ502-2-2-2-22222-2-222-2-2-2-222200002-2-222-20000-22000000002-2-220000000000000000000000000000-2200-2200
χ512-2-2-2-22222-2-222-2-2-2-22220000-222-22-20000-2200000000-222-200000000000000000000000000002-200-2200
χ522-2-2-2-22222-2-222-2-2-2-22220000-222-22-20000-2200000000-222-20000000000000000000000000000-22002-200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-400002222222200-2-200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022-2-2-2-222002200000000000000000000000000000000000000000000
χ55444-4-4-44-4400004-44-44-4-400000000000000000000000000000000000000004-40000000000000000000000
χ56444-4-4-44-4400004-44-44-4-40000000000000000000000000000000000000000-440000000000000000000000
χ5744-44-4-4-44400004-4-44-44-40000000000000000000000−2i22i2000000000000−2i22i2−2i22i2000000000000000000000000
χ5844-44-4-4-44400004-4-44-44-400000000000000000000002i2−2i20000000000002i2−2i22i2−2i2000000000000000000000000
χ5944-44-4-4-44-20000-222-22-22000000000023−2323−2300000000−2i22i200000000i6−i6i6−i6i2−i2i2−i2000000000000000000000000
χ6044-44-4-4-44-20000-222-22-22000000000023−2323−23000000002i2−2i200000000−i6i6−i6i6−i2i2−i2i2000000000000000000000000
χ6144-44-4-4-44-20000-222-22-220000000000−2323−232300000000−2i22i200000000−i6i6−i6i6i2−i2i2−i2000000000000000000000000
χ6244-44-4-4-44-20000-222-22-220000000000−2323−2323000000002i2−2i200000000i6−i6i6−i6−i2i2−i2i2000000000000000000000000
χ6344-4-444-4-444-44-444-4-4-4-4400000000-440000-44000000000000000000000000000000000000000000000000
χ6444-4-444-4-4-24-44-4-2-22222-2000000002-200002-200000000000023−2323−2300000000000000000000000000000000
χ6544-4-444-4-4-24-44-4-2-22222-2000000002-200002-2000000000000−2323−232300000000000000000000000000000000
χ6644-4-444-4-4-2-44-44-2-22222-200004i4i−4i−4i-220000-2200000000−2i−2i2i2i000000000000000000000000000000000000
χ6744-4-444-4-4-2-44-44-2-22222-20000−4i−4i4i4i-220000-22000000002i2i−2i−2i000000000000000000000000000000000000
χ684-444-44-4-4-2-444-422-2-222-24-4-4400002222-2-2-2-200-2200000000000000000000000000000000000000000000
χ694-444-44-4-4-2-444-422-2-222-2-444-4000022-2-222-2-2002-200000000000000000000000000000000000000000000
χ704-44-44-4-4440000-444-4-44-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ714-44-44-4-4440000-444-4-44-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ724-4-444-44-440000-44-444-4-400000000000000000000−2i22i20000000000−2i22i22i2−2i20000000000000000000000000000
χ734-4-444-44-440000-44-444-4-4000000000000000000002i2−2i200000000002i2−2i2−2i22i20000000000000000000000000000
χ744-4-444-44-4-200002-22-2-222000000000023−23−2323000000−2i22i20000000000i2−i2−i2i2−i6i6i6−i6000000000000000000000000
χ754-4-444-44-4-200002-22-2-222000000000023−23−23230000002i2−2i20000000000−i2i2i2−i2i6−i6−i6i6000000000000000000000000
χ764-4-444-44-4-200002-22-2-2220000000000−232323−23000000−2i22i20000000000i2−i2−i2i2i6−i6−i6i6000000000000000000000000
χ774-4-444-44-4-200002-22-2-2220000000000−232323−230000002i2−2i20000000000−i2i2i2−i2−i6i6i6−i6000000000000000000000000
χ784-4-4-4-4444444-4-4-4-4-4-444400000000-4400004-4000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-244-4-42222-2-2-2000000002-20000-22000000000000−2i32i32i3−2i300000000000000000000000000000000
χ804-4-4-4-4444-244-4-42222-2-2-2000000002-20000-220000000000002i3−2i3−2i32i300000000000000000000000000000000
χ814-4-4-4-4444-2-4-4442222-2-2-200004-4-44-2200002-200000000-222-2000000000000000000000000000000000000
χ824-4-4-4-4444-2-4-4442222-2-2-20000-444-4-2200002-2000000002-2-22000000000000000000000000000000000000
χ83888-8-8-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000

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