Finite Group Databasebeta

← Group #10849329

Character table — Group #10849329

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order12222222344446666666444444441212121212121212226666888812121212121224242424242424244444441212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-1-11-111-1-11111-1-1-1-1-1111-1-1
χ6111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1111-111-1-1-1-1-1-111111-1-1-111
χ7111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-11-1-11111-1-111-1-1-11-1-111
χ8111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-11-1-111-1-111-1-1111-111-1-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ1011111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ1111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-1-111-1-1-1-11111-1111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-1111111-1-1-1-11-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11-111-1-1-1-111-1-111-11-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-111-1-111-1-111-1-11-111-1-1
χ17222222222-2-2-2-22222222000022-2-2-2-2-22222-200000000000000-2-200000000222200000000000000-2-20000
χ18222222222-2-2-2-22222222000022-2-2-2-2-22222-200000000000000-2-200000000-2-2-2-200000000000000220000
χ19222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-2-200000000000000220000000022-2-2000000000000002-20000
χ20222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-2-2000000000000002200000000-2-22200000000000000-220000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-11111-1-2-2111122-2-2-1-1-1-111-1-1-1-1111100002-2-1-11100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-11111-1-2-21111-2-222-1-1-1-1111111-1-1-1-10000-2211-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-2111122221111-1-1-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-21111-2-2-2-21111-1-111111111000022-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-1-1-1-122-2-2111111-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-1-1-1-1-2-2221111111111-1-1-1-100002-2-1-11100000000000000
χ2922-22-22-2-22-222-222-2-22-2-22i2i−2i−2i00002-2-20000200000000002i2i−2i−2i0000000000000000000000002-20000002i−2i
χ3022-22-22-2-22-222-222-2-22-2-22i2i−2i−2i00002-2-20000200000000002i2i−2i−2i000000000000000000000000-22000000−2i2i
χ3122-22-22-2-22-222-222-2-22-2-2−2i−2i2i2i00002-2-2000020000000000−2i−2i2i2i0000000000000000000000002-2000000−2i2i
χ3222-22-22-2-22-222-222-2-22-2-2−2i−2i2i2i00002-2-2000020000000000−2i−2i2i2i000000000000000000000000-220000002i−2i
χ332-22-222-2-22-22-22-2-2222-2-22i−2i2i−2i0000-22-20000200000000002i−2i2i−2i00000000000000000000002-20000002i−2i00
χ342-22-222-2-22-22-22-2-2222-2-22i−2i2i−2i0000-22-20000200000000002i−2i2i−2i0000000000000000000000-22000000−2i2i00
χ352-22-222-2-22-22-22-2-2222-2-2−2i2i−2i2i0000-22-2000020000000000−2i2i−2i2i00000000000000000000002-2000000−2i2i00
χ362-22-222-2-22-22-22-2-2222-2-2−2i2i−2i2i0000-22-2000020000000000−2i2i−2i2i0000000000000000000000-220000002i−2i00
χ372-2-2-2-2222222-2-2-2-2-2-22222-2-222-22-2-2-2222-2-222-222-2-200002-2-222-200000000000000000000000000000000
χ382-2-2-2-2222222-2-2-2-2-2-22222-2-22-22-22-2-22-2-2222-22-2-22200002-2-22-2200000000000000000000000000000000
χ392-2-2-2-2222222-2-2-2-2-2-2222-222-22-22-2-2-2222-2-22-22-2-2220000-222-22-200000000000000000000000000000000
χ402-2-2-2-2222222-2-2-2-2-2-2222-222-2-22-22-2-22-2-22222-222-2-20000-222-2-2200000000000000000000000000000000
χ412-2-2-2-22222-2-222-2-2-2-222200002-2-2222-222-2-2-200000000000000-220000000000000000002-200002-2000000
χ422-2-2-2-22222-2-222-2-2-2-222200002-2-2222-222-2-2-200000000000000-22000000000000000000-220000-22000000
χ432-2-2-2-22222-2-222-2-2-2-22220000-222-222-2-2-222-2000000000000002-20000000000000000002-20000-22000000
χ442-2-2-2-22222-2-222-2-2-2-22220000-222-222-2-2-222-2000000000000002-2000000000000000000-2200002-2000000
χ452-2-2-2-2222-122-2-21111-1-1-12-2-222-22-211-1-1-111-12-2-1-1110000-111-1-11−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i300000000000000
χ462-2-2-2-2222-122-2-21111-1-1-12-2-222-22-211-1-1-111-12-2-1-1110000-111-1-11i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i300000000000000
χ472-2-2-2-2222-122-2-21111-1-1-12-2-22-22-2211-111-1-1-1-2211-1-10000-111-11-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i300000000000000
χ482-2-2-2-2222-122-2-21111-1-1-12-2-22-22-2211-111-1-1-1-2211-1-10000-111-11-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i300000000000000
χ492-2-2-2-2222-122-2-21111-1-1-1-222-22-22-211-1-1-111-1-2211-1-100001-1-11-11−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i300000000000000
χ502-2-2-2-2222-122-2-21111-1-1-1-222-22-22-211-1-1-111-1-2211-1-100001-1-11-11i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i300000000000000
χ512-2-2-2-2222-122-2-21111-1-1-1-222-2-22-2211-111-1-1-12-2-1-11100001-1-111-1−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i300000000000000
χ522-2-2-2-2222-122-2-21111-1-1-1-222-2-22-2211-111-1-1-12-2-1-11100001-1-111-1i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i300000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4222-2-2-2-22000000000000002200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4442222222200000000000000-2-200000000000000000000000000000000
χ55444-4-4-4-44400004-44-4-4-4400000000000000000000000000000000000000004i−4i0000000000000000000000
χ56444-4-4-4-44400004-44-4-4-440000000000000000000000000000000000000000−4i4i0000000000000000000000
χ5744-44-44-4-444-4-4444-4-44-4-400000000-4440000-4000000000000000000000000000000000000000000000000
χ5844-44-44-4-4-24-4-44-2-222-222000000002-2-20000200−2i32i3−2i32i3000000000000000000000000000000000000000000
χ5944-44-44-4-4-24-4-44-2-222-222000000002-2-200002002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ6044-44-44-4-4-2-444-4-2-222-2224i4i−4i−4i0000-2220000-20000000000−2i−2i2i2i0000000000000000000000000000000000
χ6144-44-44-4-4-2-444-4-2-222-222−4i−4i4i4i0000-2220000-200000000002i2i−2i−2i0000000000000000000000000000000000
χ6244-4-44-44-4400004-4-44-44-4000000000000000000000000−2i22i20000000000−2i22i2−2i22i2000000000000000000000000
χ6344-4-44-44-4400004-4-44-44-40000000000000000000000002i2−2i200000000002i2−2i22i2−2i2000000000000000000000000
χ6444-4-44-44-4-20000-222-22-2200000000000−2i32i3−2i32i3000000000−2i22i20000006−66−6i2−i2i2−i2000000000000000000000000
χ6544-4-44-44-4-20000-222-22-2200000000000−2i32i3−2i32i30000000002i2−2i2000000−66−66−i2i2−i2i2000000000000000000000000
χ6644-4-44-44-4-20000-222-22-22000000000002i3−2i32i3−2i3000000000−2i22i2000000−66−66i2−i2i2−i2000000000000000000000000
χ6744-4-44-44-4-20000-222-22-22000000000002i3−2i32i3−2i30000000002i2−2i20000006−66−6−i2i2−i2i2000000000000000000000000
χ684-444-4-44-440000-444-4-44-40000000000000000000000−2i22i200000000−2i22i22i2−2i20000000000000000000000000000
χ694-444-4-44-440000-444-4-44-400000000000000000000002i2−2i2000000002i2−2i2−2i22i20000000000000000000000000000
χ704-444-4-44-4-200002-2-222-2200000000000−2i32i32i3−2i30000000−2i22i200000000i2−i2−i2i26−6−66000000000000000000000000
χ714-444-4-44-4-200002-2-222-2200000000000−2i32i32i3−2i300000002i2−2i200000000−i2i2i2−i2−666−6000000000000000000000000
χ724-444-4-44-4-200002-2-222-22000000000002i3−2i3−2i32i30000000−2i22i200000000i2−i2−i2i2−666−6000000000000000000000000
χ734-444-4-44-4-200002-2-222-22000000000002i3−2i3−2i32i300000002i2−2i200000000−i2i2i2−i26−6−66000000000000000000000000
χ744-44-444-4-444-44-4-4-4444-4-4000000004-440000-4000000000000000000000000000000000000000000000000
χ754-44-444-4-4-24-44-422-2-2-22200000000-22-20000200−2i32i32i3−2i3000000000000000000000000000000000000000000
χ764-44-444-4-4-24-44-422-2-2-22200000000-22-200002002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ774-44-444-4-4-2-44-4422-2-2-2224i−4i4i−4i00002-220000-20000000000−2i2i−2i2i0000000000000000000000000000000000
χ784-44-444-4-4-2-44-4422-2-2-222−4i4i−4i4i00002-220000-200000000002i−2i2i−2i0000000000000000000000000000000000
χ794-4-444-4-4440000-44-44-4-440000000000000000000000000000000000000000004-400000000000000000000
χ804-4-444-4-4440000-44-44-4-44000000000000000000000000000000000000000000-4400000000000000000000
χ814-4-4-4-4444-2-4-4442222-2-2-200004-4-44-2-22-2-2222000000000000002-200000000000000000000000000000000
χ824-4-4-4-4444-2-4-4442222-2-2-20000-444-4-2-2222-2-2200000000000000-2200000000000000000000000000000000
χ83888-8-8-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000

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