Finite Group Databasebeta

← Group #10876066

Character table — Group #10876066

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666644444444121212121212121244888812121212121212121212242424242424242444442466121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-1-1111-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-1-1-1-1111-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-1-1-1-11111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-11111111-1-1-1-1-1-1-111
χ911111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ1011111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-11111-1-1-1-1
χ1111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111-1-1-1111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-111111-1-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-111-1111-1-1-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-1-1-11-1-1-11111-1-111
χ17222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-2-2-200000000002200000000000022-2-200000000200-200000000
χ18222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-2-2-2000000000022000000000000-2-22200000000-200200000000
χ19222222222-2-2-2-222222220000-2-2222222-2-2-2-20000000000-2-2000000000000222200000000-200-200000000
χ20222222222-2-2-2-222222220000-2-2222222-2-2-2-20000000000-2-2000000000000-2-2-2-200000000200200000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-1-2-222-2-2-1-1-1-1111111-1-1-1-1111100002-2-1-11100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-1-2-2-2-222-1-1-1-11111111111-1-1-1-10000-2211-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-222221111-1-11111-1-1-1-1-1-1-1-10000-2-2111100000000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-12222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
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
χ29222-2-22-2-22-22-222-2-2-222-222-2-200000000-2-22200000022-2-2000000000000000000000000000000002i−2i2i−2i00
χ30222-2-22-2-22-22-222-2-2-222-222-2-200000000-2-22200000022-2-200000000000000000000000000000000−2i2i−2i2i00
χ31222-2-22-2-22-22-222-2-2-222-2-2-22200000000-2-222000000-2-222000000000000000000000000000000002i−2i−2i2i00
χ32222-2-22-2-22-22-222-2-2-222-2-2-22200000000-2-222000000-2-22200000000000000000000000000000000−2i2i2i−2i00
χ332-222-2-2-2222-2-22-222-2-22-200002i−2i2i−2i2i2i−2i−2i2-22-200000000002i−2i00000000000000000000000002i−2i02-2000000
χ342-222-2-2-2222-2-22-222-2-22-200002i−2i2i−2i2i2i−2i−2i2-22-200000000002i−2i0000000000000000000000000−2i2i0-22000000
χ352-222-2-2-2222-2-22-222-2-22-20000−2i2i−2i2i−2i−2i2i2i2-22-20000000000−2i2i00000000000000000000000002i−2i0-22000000
χ362-222-2-2-2222-2-22-222-2-22-20000−2i2i−2i2i−2i−2i2i2i2-22-20000000000−2i2i0000000000000000000000000−2i2i02-2000000
χ372-222-2-2-222-222-2-222-2-22-22-22-22i−2i−2i2i−2i−2i2i2i-22-222i−2i00002-22-22i−2i2i2i−2i−2i00000000000000000000000000000000
χ382-222-2-2-222-222-2-222-2-22-22-22-2−2i2i2i−2i2i2i−2i−2i-22-22−2i2i00002-22-2−2i2i−2i−2i2i2i00000000000000000000000000000000
χ392-222-2-2-222-222-2-222-2-22-2-22-222i−2i−2i2i−2i−2i2i2i-22-22−2i2i0000-22-222i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-222-2-2-222-222-2-222-2-22-2-22-22−2i2i2i−2i2i2i−2i−2i-22-222i−2i0000-22-22−2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-222-2-2-22-1-222-21-1-111-112-22-22i−2i−2i2iii−i−i1-11-12i−2i0000-11-11−ii−i−iii−i3−i3i3i333−3−3000000−i3i33−300000000000000
χ422-222-2-2-22-1-222-21-1-111-112-22-22i−2i−2i2iii−i−i1-11-12i−2i0000-11-11−ii−i−iiii3i3−i3−i3−3−333000000i3−i3−3300000000000000
χ432-222-2-2-22-1-222-21-1-111-112-22-2−2i2i2i−2i−i−iii1-11-1−2i2i0000-11-11i−iii−i−i−i3−i3i3i3−3−333000000−i3i3−3300000000000000
χ442-222-2-2-22-1-222-21-1-111-112-22-2−2i2i2i−2i−i−iii1-11-1−2i2i0000-11-11i−iii−i−ii3i3−i3−i333−3−3000000i3−i33−300000000000000
χ452-222-2-2-22-1-222-21-1-111-11-22-222i−2i−2i2iii−i−i1-11-1−2i2i00001-11-1−iiii−i−i−i3−i3i3i333−3−3000000i3−i3−3300000000000000
χ462-222-2-2-22-1-222-21-1-111-11-22-222i−2i−2i2iii−i−i1-11-1−2i2i00001-11-1−iiii−i−ii3i3−i3−i3−3−333000000−i3i33−300000000000000
χ472-222-2-2-22-1-222-21-1-111-11-22-22−2i2i2i−2i−i−iii1-11-12i−2i00001-11-1i−i−i−iii−i3−i3i3i3−3−333000000i3−i33−300000000000000
χ482-222-2-2-22-1-222-21-1-111-11-22-22−2i2i2i−2i−i−iii1-11-12i−2i00001-11-1i−i−i−iiii3i3−i3−i333−3−3000000−i3i3−3300000000000000
χ492-22-22-22-2222-2-2-2-2-22-2222-2-22000000002-2-220000002-2-220000000000000000000000002i−2i00000000002i−2i
χ502-22-22-22-2222-2-2-2-2-22-2222-2-22000000002-2-220000002-2-22000000000000000000000000−2i2i0000000000−2i2i
χ512-22-22-22-2222-2-2-2-2-22-222-222-2000000002-2-22000000-222-20000000000000000000000002i−2i0000000000−2i2i
χ522-22-22-22-2222-2-2-2-2-22-222-222-2000000002-2-22000000-222-2000000000000000000000000−2i2i00000000002i−2i
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4222222220000000000-2-2000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-444-2-2-2-22222000000000022000000000000000000000000000000000000
χ55444-4-44-4-444-44-44-4-4-444-400000000000044-4-4000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-24-44-4-2222-2-22000000000000-2-22200000000000023−2323−2300000000000000000000000000000000
χ57444-4-44-4-4-24-44-4-2222-2-22000000000000-2-222000000000000−2323−232300000000000000000000000000000000
χ58444-4-44-4-4-2-44-44-2222-2-2244-4-40000000022-2-2000000-2-22200000000000000000000000000000000000000
χ59444-4-44-4-4-2-44-44-2222-2-22-4-4440000000022-2-200000022-2-200000000000000000000000000000000000000
χ6044-444-4-4-44000044-4-4-4-440000000000000000000022−220000000000000022−2222−22000000000000000000000000
χ6144-444-4-4-44000044-4-4-4-4400000000000000000000−222200000000000000−2222−2222000000000000000000000000
χ6244-444-4-4-4-20000-2-22222-20000000023−2323−230000000022−2200000000006−66−6−22−22000000000000000000000000
χ6344-444-4-4-4-20000-2-22222-20000000023−2323−2300000000−22220000000000−66−662−22−2000000000000000000000000
χ6444-444-4-4-4-20000-2-22222-200000000−2323−23230000000022−220000000000−66−66−22−22000000000000000000000000
χ6544-444-4-4-4-20000-2-22222-200000000−2323−232300000000−222200000000006−66−62−22−2000000000000000000000000
χ6644-4-4-4-444400004-444-4-4-400000000000000000000000000000000000000004i−4i0000000000000000000000
χ6744-4-4-4-444400004-444-4-4-40000000000000000000000000000000000000000−4i4i0000000000000000000000
χ684-444-4-4-44-24-4-442-2-222-2200004i−4i4i−4i−2i−2i2i2i-22-220000000000−2i2i000000000000000000000000000000000000
χ694-444-4-4-44-24-4-442-2-222-220000−4i4i−4i4i2i2i−2i−2i-22-2200000000002i−2i000000000000000000000000000000000000
χ704-44-44-44-44-4-444-4-4-44-444000000000000-444-4000000000000000000000000000000000000000000000000
χ714-44-44-44-4-244-4-4222-22-2-24-4-4400000000-222-2000000-222-200000000000000000000000000000000000000
χ724-44-44-44-4-244-4-4222-22-2-2-444-400000000-222-20000002-2-2200000000000000000000000000000000000000
χ734-44-44-44-4-2-4-444222-22-2-20000000000002-2-22000000000000−2i32i32i3−2i300000000000000000000000000000000
χ744-44-44-44-4-2-4-444222-22-2-20000000000002-2-220000000000002i3−2i3−2i32i300000000000000000000000000000000
χ754-4-44-444-440000-44-444-4-4000000000000000000−2i22i2000000000000−2i22i22i2−2i20000000000000000000000000000
χ764-4-44-444-440000-44-444-4-40000000000000000002i2−2i20000000000002i2−2i2−2i22i20000000000000000000000000000
χ774-4-44-444-4-200002-22-2-22200000000−2i32i32i3−2i3000000−2i22i2000000000000i2−i2−i2i2−666−6000000000000000000000000
χ784-4-44-444-4-200002-22-2-22200000000−2i32i32i3−2i30000002i2−2i2000000000000−i2i2i2−i26−6−66000000000000000000000000
χ794-4-44-444-4-200002-22-2-222000000002i3−2i3−2i32i3000000−2i22i2000000000000i2−i2−i2i26−6−66000000000000000000000000
χ804-4-44-444-4-200002-22-2-222000000002i3−2i3−2i32i30000002i2−2i2000000000000−i2i2i2−i2−666−6000000000000000000000000
χ814-4-4-444-4440000-4-44-44-440000000000000000000000000000000000000000004-400000000000000000000
χ824-4-4-444-4440000-4-44-44-44000000000000000000000000000000000000000000-4400000000000000000000
χ8388-8-8-8-888-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000

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