Finite Group Databasebeta

← Group #10868296

Character table — Group #10868296

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order122222223444466666664444444412121212121212124488881212121212121212121224242424242424244444441212121224444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-11-1-111-111-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-1111-1-111-111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11-111-1-1-111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111-111-1-11-1-1-1-1-1111111-1-1
χ911111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ1011111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1
χ1111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-111-1-1-1-1-111111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-111-1-1111-1-1-1-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-111-1-1-1-1-111111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1-11111111-1-1-1-1-111-1-1
χ17222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-2-2-200000000002200000000000022-2-200000020000-200000000
χ18222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-2-2-2000000000022000000000000-2-222000000-20000200000000
χ19222222222-2-2-2-222222220000-2-222-2-22222-2-20000000000-2-20000000000002222000000-20000-200000000
χ20222222222-2-2-2-222222220000-2-222-2-22222-2-20000000000-2-2000000000000-2-2-2-200000020000200000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-11111-1-1-2-222-2-2-1-1-1-1111111-1-1-1-111110000-2211-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-11111-1-1-2-2-2-222-1-1-1-11111111111-1-1-1-100002-2-1-11100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-222221111-1-11111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1111111111111000022-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-12222-2-2111111-1-1-1-1-1-1-1-1111100002-2-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-2-222111111-1-1-1-11111-1-1-1-10000-2211-1-100000000000000
χ2922-22-2-22-2222-2-2-2-2-2-222222-2-200002-200002-200000022-2-2000000000000000000000000000000002i−2i2i−2i00
χ3022-22-2-22-2222-2-2-2-2-2-222222-2-200002-200002-200000022-2-200000000000000000000000000000000−2i2i−2i2i00
χ3122-22-2-22-2222-2-2-2-2-2-2222-2-22200002-200002-2000000-2-222000000000000000000000000000000002i−2i−2i2i00
χ3222-22-2-22-2222-2-2-2-2-2-2222-2-22200002-200002-2000000-2-22200000000000000000000000000000000−2i2i2i−2i00
χ332-222-2-2-222-22-2222-2-22-2-22i−2i2i−2i0000-2-20000220000002i−2i2i−2i0000000000000000000000000002i−2i00000002-2
χ342-222-2-2-222-22-2222-2-22-2-22i−2i2i−2i0000-2-20000220000002i−2i2i−2i000000000000000000000000000−2i2i0000000-22
χ352-222-2-2-222-22-2222-2-22-2-2−2i2i−2i2i0000-2-2000022000000−2i2i−2i2i0000000000000000000000000002i−2i0000000-22
χ362-222-2-2-222-22-2222-2-22-2-2−2i2i−2i2i0000-2-2000022000000−2i2i−2i2i000000000000000000000000000−2i2i00000002-2
χ372-2-2222-2-222-2-22-2-2222-2-200002i−2i2i−2i2-22i2i−2i−2i-2200000000002i−2i000000000000000000000002-20002i−2i000000
χ382-2-2222-2-222-2-22-2-2222-2-200002i−2i2i−2i2-22i2i−2i−2i-2200000000002i−2i00000000000000000000000-22000−2i2i000000
χ392-2-2222-2-222-2-22-2-2222-2-20000−2i2i−2i2i2-2−2i−2i2i2i-220000000000−2i2i000000000000000000000002-2000−2i2i000000
χ402-2-2222-2-222-2-22-2-2222-2-20000−2i2i−2i2i2-2−2i−2i2i2i-220000000000−2i2i00000000000000000000000-220002i−2i000000
χ412-2-2222-2-22-222-2-2-2222-2-22i−2i−2i2i2i−2i−2i2i-22−2i−2i2i2i2-22-200002i−2i−2i2i2i−2i22-2-200000000000000000000000000000000
χ422-2-2222-2-22-222-2-2-2222-2-22i−2i−2i2i−2i2i2i−2i-222i2i−2i−2i2-2-2200002i−2i−2i2i−2i2i-2-22200000000000000000000000000000000
χ432-2-2222-2-22-222-2-2-2222-2-2−2i2i2i−2i2i−2i−2i2i-22−2i−2i2i2i2-2-220000−2i2i2i−2i2i−2i-2-22200000000000000000000000000000000
χ442-2-2222-2-22-222-2-2-2222-2-2−2i2i2i−2i−2i2i2i−2i-222i2i−2i−2i2-22-20000−2i2i2i−2i−2i2i22-2-200000000000000000000000000000000
χ452-2-2222-2-2-1-222-211-1-1-1112i−2i−2i2i2i−2i−2i2i1-1ii−i−i-112-20000−iii−i−ii-1-111−i3−i3i3i333−3−3000000−i3i33−300000000000000
χ462-2-2222-2-2-1-222-211-1-1-1112i−2i−2i2i2i−2i−2i2i1-1ii−i−i-112-20000−iii−i−ii-1-111i3i3−i3−i3−3−333000000i3−i3−3300000000000000
χ472-2-2222-2-2-1-222-211-1-1-1112i−2i−2i2i−2i2i2i−2i1-1−i−iii-11-220000−iii−ii−i11-1-1−i3−i3i3i3−3−333000000i3−i33−300000000000000
χ482-2-2222-2-2-1-222-211-1-1-1112i−2i−2i2i−2i2i2i−2i1-1−i−iii-11-220000−iii−ii−i11-1-1i3i3−i3−i333−3−3000000−i3i3−3300000000000000
χ492-2-2222-2-2-1-222-211-1-1-111−2i2i2i−2i2i−2i−2i2i1-1ii−i−i-11-220000i−i−ii−ii11-1-1−i3−i3i3i333−3−3000000i3−i3−3300000000000000
χ502-2-2222-2-2-1-222-211-1-1-111−2i2i2i−2i2i−2i−2i2i1-1ii−i−i-11-220000i−i−ii−ii11-1-1i3i3−i3−i3−3−333000000−i3i33−300000000000000
χ512-2-2222-2-2-1-222-211-1-1-111−2i2i2i−2i−2i2i2i−2i1-1−i−iii-112-20000i−i−iii−i-1-111−i3−i3i3i3−3−333000000−i3i3−3300000000000000
χ522-2-2222-2-2-1-222-211-1-1-111−2i2i2i−2i−2i2i2i−2i1-1−i−iii-112-20000i−i−iii−i-1-111i3i3−i3−i333−3−3000000i3−i33−300000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4222222220000000000-2-2000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-44422-2-2-2-222000000000022000000000000000000000000000000000000
χ55444-44-4-4-4400004-44-4-44-400000000000000000000000000000000000000004-40000000000000000000000
χ56444-44-4-4-4400004-44-4-44-40000000000000000000000000000000000000000-440000000000000000000000
χ5744-44-4-44-44-4-444-4-4-4-444400000000-440000-44000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-244-4-42222-2-2-244-4-40000-220000-22000000-2-22200000000000000000000000000000000000000
χ5944-44-4-44-4-244-4-42222-2-2-2-4-4440000-220000-2200000022-2-200000000000000000000000000000000000000
χ6044-44-4-44-4-2-4-4442222-2-2-2000000002-200002-2000000000000−2i32i3−2i32i300000000000000000000000000000000
χ6144-44-4-44-4-2-4-4442222-2-2-2000000002-200002-20000000000002i3−2i32i3−2i300000000000000000000000000000000
χ6244-4-4-44-4440000-44-44-44-4000000000000000000−2i22i2000000000000−2i22i2−2i22i20000000000000000000000000000
χ6344-4-4-44-4440000-44-44-44-40000000000000000002i2−2i20000000000002i2−2i22i2−2i20000000000000000000000000000
χ6444-4-4-44-44-200002-22-22-22000000000023−2323−230000−2i22i2000000000000i2−i2i2−i2i6−i6i6−i6000000000000000000000000
χ6544-4-4-44-44-200002-22-22-22000000000023−2323−2300002i2−2i2000000000000−i2i2−i2i2−i6i6−i6i6000000000000000000000000
χ6644-4-4-44-44-200002-22-22-220000000000−2323−23230000−2i22i2000000000000i2−i2i2−i2−i6i6−i6i6000000000000000000000000
χ6744-4-4-44-44-200002-22-22-220000000000−2323−232300002i2−2i2000000000000−i2i2−i2i2i6−i6i6−i6000000000000000000000000
χ684-444-4-4-4444-44-444-4-44-4-400000000440000-4-4000000000000000000000000000000000000000000000000
χ694-444-4-4-44-24-44-4-2-222-22200000000-2-2000022000000000000−2i32i32i3−2i300000000000000000000000000000000
χ704-444-4-4-44-24-44-4-2-222-22200000000-2-20000220000000000002i3−2i3−2i32i300000000000000000000000000000000
χ714-444-4-4-44-2-44-44-2-222-2224i−4i4i−4i0000220000-2-2000000−2i2i−2i2i00000000000000000000000000000000000000
χ724-444-4-4-44-2-44-44-2-222-222−4i4i−4i4i0000220000-2-20000002i−2i2i−2i00000000000000000000000000000000000000
χ734-44-4-444-4400004-4-44-4-4400000000000000000000−2i22i200000000000000−2i22i22i2−2i2000000000000000000000000
χ744-44-4-444-4400004-4-44-4-44000000000000000000002i2−2i2000000000000002i2−2i2−2i22i2000000000000000000000000
χ754-44-4-444-4-20000-222-222-20000000000−2i32i32i3−2i3000000−2i22i20000000000−666−6i2−i2−i2i2000000000000000000000000
χ764-44-4-444-4-20000-222-222-20000000000−2i32i32i3−2i30000002i2−2i200000000006−6−66−i2i2i2−i2000000000000000000000000
χ774-44-4-444-4-20000-222-222-200000000002i3−2i3−2i32i3000000−2i22i200000000006−6−66i2−i2−i2i2000000000000000000000000
χ784-44-4-444-4-20000-222-222-200000000002i3−2i3−2i32i30000002i2−2i20000000000−666−6−i2i2i2−i2000000000000000000000000
χ794-4-4444-4-4-24-4-4422-2-2-22200004i−4i4i−4i-22−2i−2i2i2i2-20000000000−2i2i000000000000000000000000000000000000
χ804-4-4444-4-4-24-4-4422-2-2-2220000−4i4i−4i4i-222i2i−2i−2i2-200000000002i−2i000000000000000000000000000000000000
χ814-4-4-44-44440000-444-4-4-440000000000000000000000000000000000000000004i−4i00000000000000000000
χ824-4-4-44-44440000-444-4-4-44000000000000000000000000000000000000000000−4i4i00000000000000000000
χ83888-88-8-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-88-888-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000

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