Finite Group Databasebeta

← Group #10853242

Character table — Group #10853242

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order12222222344446666666224444446666121212124488881212121212121212121224242424242424244444441212121244444444448888
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
χ5111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ6111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-1-11111
χ911111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-11-1-111-111-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-1-111-1-11-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-1111-1-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1-111-111111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111111-1-1-1-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-111-1-1-111111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-111111-1-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-1-1-1-1-1-11111111-1-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-200000000000000002222000000-20000-200000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-20000000000000000-2-2-2-200000020000200000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-200000022000000000000000022-2-2000000-20000200000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-2000000220000000000000000-2-22200000020000-200000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2-222-2-211-1-1-1-11111-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2-2-2-22211-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-12222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-122-2-222111111-1-1-1-11111-1-1-1-100002-2-1-11100000000000000
χ292222-2-2-2-2222-2-22-2-22-2-222-22-222-2-222-2-222-2-22-200002-222-2-222-2-200000000000000000000000000000000
χ302222-2-2-2-2222-2-22-2-22-2-222-22-2-2-22222-2-222-2-2-2200002-2-2-222-2-22200000000000000000000000000000000
χ312222-2-2-2-2222-2-22-2-22-2-22-22-2222-2-2-2-22222-2-2-220000-2222-2-2-2-22200000000000000000000000000000000
χ322222-2-2-2-2222-2-22-2-22-2-22-22-22-2-222-2-22222-2-22-20000-22-2-22222-2-200000000000000000000000000000000
χ332222-2-2-2-22-2-2222-2-22-2-222-2-22000022-2-2-2-222000000-220000000000000000000000000002i−2i0002i−2i000000
χ342222-2-2-2-22-2-2222-2-22-2-222-2-22000022-2-2-2-222000000-22000000000000000000000000000−2i2i000−2i2i000000
χ352222-2-2-2-22-2-2222-2-22-2-22-222-20000-2-222-2-2220000002-20000000000000000000000000002i−2i000−2i2i000000
χ362222-2-2-2-22-2-2222-2-22-2-22-222-20000-2-222-2-2220000002-2000000000000000000000000000−2i2i0002i−2i000000
χ372222-2-2-2-2-122-2-2-111-111-12-22-222-2-2-1-111-1-1112-20000-11-1-111-1-11133−3−333−3−30000003−33−300000000000000
χ382222-2-2-2-2-122-2-2-111-111-12-22-222-2-2-1-111-1-1112-20000-11-1-111-1-111−3−333−3−333000000−33−3300000000000000
χ392222-2-2-2-2-122-2-2-111-111-12-22-2-2-222-1-111-1-111-220000-1111-1-111-1-133−3−333−3−3000000−33−3300000000000000
χ402222-2-2-2-2-122-2-2-111-111-12-22-2-2-222-1-111-1-111-220000-1111-1-111-1-1−3−333−3−3330000003−33−300000000000000
χ412222-2-2-2-2-122-2-2-111-111-1-22-2222-2-211-1-1-1-111-2200001-1-1-11111-1-133−3−3−3−3330000003−3−3300000000000000
χ422222-2-2-2-2-122-2-2-111-111-1-22-2222-2-211-1-1-1-111-2200001-1-1-11111-1-1−3−33333−3−3000000−333−300000000000000
χ432222-2-2-2-2-122-2-2-111-111-1-22-22-2-22211-1-1-1-1112-200001-111-1-1-1-11133−3−3−3−333000000−333−300000000000000
χ442222-2-2-2-2-122-2-2-111-111-1-22-22-2-22211-1-1-1-1112-200001-111-1-1-1-111−3−33333−3−30000003−3−3300000000000000
χ452-22-222-2-222-2-22-22-222-2-200002i−2i2i−2i00002-22-2000000002i−2i2i−2i0000000000000000000000000000002i−2i002-2
χ462-22-222-2-222-2-22-22-222-2-200002i−2i2i−2i00002-22-2000000002i−2i2i−2i000000000000000000000000000000−2i2i00-22
χ472-22-222-2-222-2-22-22-222-2-20000−2i2i−2i2i00002-22-200000000−2i2i−2i2i0000000000000000000000000000002i−2i00-22
χ482-22-222-2-222-2-22-22-222-2-20000−2i2i−2i2i00002-22-200000000−2i2i−2i2i000000000000000000000000000000−2i2i002-2
χ492-22-2-2-22222-22-2-2-222-22-200002i−2i−2i2i00002-2-22000000002i−2i−2i2i00000000000000000000000002-2000002i−2i00
χ502-22-2-2-22222-22-2-2-222-22-200002i−2i−2i2i00002-2-22000000002i−2i−2i2i0000000000000000000000000-2200000−2i2i00
χ512-22-2-2-22222-22-2-2-222-22-20000−2i2i2i−2i00002-2-2200000000−2i2i2i−2i00000000000000000000000002-200000−2i2i00
χ522-22-2-2-22222-22-2-2-222-22-20000−2i2i2i−2i00002-2-2200000000−2i2i2i−2i0000000000000000000000000-22000002i−2i00
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000-2-2-2-22222000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022222222000000-2-20000000000000000000000000000000000000000
χ554444-4-4-4-4-2-4-444-222-222-24-4-440000-2-22222-2-20000002-20000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-444-222-222-2-444-4000022-2-222-2-2000000-220000000000000000000000000000000000000000
χ5744-4-44-44-4400004-44-44-4-400000000000000000000000000000000000000004-40000000000000000000000
χ5844-4-44-44-4400004-44-44-4-40000000000000000000000000000000000000000-440000000000000000000000
χ5944-4-4-44-444000044-4-4-44-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ6044-4-4-44-444000044-4-4-44-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ614-44-444-4-44-444-4-44-444-4-4000000000000-44-44000000000000000000000000000000000000000000000000
χ624-44-444-4-4-24-4-442-22-2-22200004i−4i4i−4i0000-22-2200000000−2i2i−2i2i000000000000000000000000000000000000
χ634-44-444-4-4-24-4-442-22-2-2220000−4i4i−4i4i0000-22-22000000002i−2i2i−2i000000000000000000000000000000000000
χ644-44-444-4-4-2-444-42-22-2-2220000000000002-22-200000000000023−2323−2300000000000000000000000000000000
χ654-44-444-4-4-2-444-42-22-2-2220000000000002-22-2000000000000−2323−232300000000000000000000000000000000
χ664-44-4-4-4444-44-44-4-444-44-4000000000000-444-4000000000000000000000000000000000000000000000000
χ674-44-4-4-444-24-44-422-2-22-2200004i−4i−4i4i0000-222-200000000−2i2i2i−2i000000000000000000000000000000000000
χ684-44-4-4-444-24-44-422-2-22-220000−4i4i4i−4i0000-222-2000000002i−2i−2i2i000000000000000000000000000000000000
χ694-44-4-4-444-2-44-4422-2-22-220000000000002-2-2200000000000023−23−232300000000000000000000000000000000
χ704-44-4-4-444-2-44-4422-2-22-220000000000002-2-22000000000000−232323−2300000000000000000000000000000000
χ714-4-444-4-4440000-4-4-4-44440000000000000000000022−220000000000000022−2222−22000000000000000000000000
χ724-4-444-4-4440000-4-4-4-444400000000000000000000−222200000000000000−2222−2222000000000000000000000000
χ734-4-444-4-44-200002222-2-2-200000000−2i32i3−2i32i30000000022−220000000000i6−i6i6−i6−22−22000000000000000000000000
χ744-4-444-4-44-200002222-2-2-200000000−2i32i3−2i32i300000000−22220000000000−i6i6−i6i62−22−2000000000000000000000000
χ754-4-444-4-44-200002222-2-2-2000000002i3−2i32i3−2i30000000022−220000000000−i6i6−i6i6−22−22000000000000000000000000
χ764-4-444-4-44-200002222-2-2-2000000002i3−2i32i3−2i300000000−22220000000000i6−i6i6−i62−22−2000000000000000000000000
χ774-4-44-444-440000-444-4-4-44000000000000000000−2i22i2000000000000−2i22i22i2−2i20000000000000000000000000000
χ784-4-44-444-440000-444-4-4-440000000000000000002i2−2i20000000000002i2−2i2−2i22i20000000000000000000000000000
χ794-4-44-444-4-200002-2-2222-200000000−2i32i32i3−2i3000000−2i22i2000000000000i2−i2−i2i26−6−66000000000000000000000000
χ804-4-44-444-4-200002-2-2222-200000000−2i32i32i3−2i30000002i2−2i2000000000000−i2i2i2−i2−666−6000000000000000000000000
χ814-4-44-444-4-200002-2-2222-2000000002i3−2i3−2i32i3000000−2i22i2000000000000i2−i2−i2i2−666−6000000000000000000000000
χ824-4-44-444-4-200002-2-2222-2000000002i3−2i3−2i32i30000002i2−2i2000000000000−i2i2i2−i26−6−66000000000000000000000000
χ8388-8-88-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000

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