Finite Group Databasebeta

← Group #10845255

Character table — Group #10845255

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order122222223444466666664444444412121212121212124488881212121212121212121224242424242424244444441212121222224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1-11-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111
χ5111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111
χ6111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-11111
χ911111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-1-1-111-111-1-1111-1-1
χ1011111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-111-1-11-1-111-1-1-111
χ1111111111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-1-1-1-111111-1-111
χ1211111111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1-11111111-1-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-11111-1-1-1-1-111111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-111-1-111111-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-11111-1-1-1-1-11-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-1-1-1-1-111111-111-1-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-22222-2000000-2-2000000000000000022220000000000-20000-20000
χ18222222222-2-2-2-2222222222-2-20000-2-2-22222-2000000-2-20000000000000000-2-2-2-200000000002000020000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-200000022000000000000000022-2-2000000000020000-20000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-2000000220000000000000000-2-2220000000000-2000020000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-1-2-222-2-211-1-1-1-11111-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-1-2-2-2-22211-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-12222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-2-222111111-1-1-1-11111-1-1-1-100002-2-1-11100000000000000
χ29222-2-22-2-222-2-222-22-22-2-200002i2i−2i−2i2-2-200002000000002i2i−2i−2i0000000000000000000000002-20000002i−2i00
χ30222-2-22-2-222-2-222-22-22-2-200002i2i−2i−2i2-2-200002000000002i2i−2i−2i000000000000000000000000-22000000−2i2i00
χ31222-2-22-2-222-2-222-22-22-2-20000−2i−2i2i2i2-2-20000200000000−2i−2i2i2i0000000000000000000000002-2000000−2i2i00
χ32222-2-22-2-222-2-222-22-22-2-20000−2i−2i2i2i2-2-20000200000000−2i−2i2i2i000000000000000000000000-220000002i−2i00
χ332-2-22-222-2222-2-2-2-222-2-222-22-22i−2i2i−2i22-222-2-2-22i−2i00002-22i−2i2i−2i2i2i−2i−2i00000000000000000000000000000000
χ342-2-22-222-2222-2-2-2-222-2-222-22-2−2i2i−2i2i22-222-2-2-2−2i2i00002-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000
χ352-2-22-222-2222-2-2-2-222-2-22-22-222i−2i2i−2i22-2-2-222-2−2i2i0000-222i−2i2i−2i−2i−2i2i2i00000000000000000000000000000000
χ362-2-22-222-2222-2-2-2-222-2-22-22-22−2i2i−2i2i22-2-2-222-22i−2i0000-22−2i2i−2i2i2i2i−2i−2i00000000000000000000000000000000
χ372-2-22-222-22-2-222-2-222-2-222-2-220000-2-2222-2-22000000-22000000000000000000000000002-20002-20000000
χ382-2-22-222-22-2-222-2-222-2-222-2-220000-2-2222-2-22000000-2200000000000000000000000000-22000-220000000
χ392-2-22-222-22-2-222-2-222-2-22-222-20000-2-22-2-22220000002-2000000000000000000000000002-2000-220000000
χ402-2-22-222-22-2-222-2-222-2-22-222-20000-2-22-2-22220000002-200000000000000000000000000-220002-20000000
χ412-2-22-222-2-122-2-211-1-111-12-22-22i−2i2i−2i-1-11-1-11112i−2i0000-11−ii−ii−i−iii33−3−333−3−3000000−i3i3−i3i300000000000000
χ422-2-22-222-2-122-2-211-1-111-12-22-22i−2i2i−2i-1-11-1-11112i−2i0000-11−ii−ii−i−iii−3−333−3−333000000i3−i3i3−i300000000000000
χ432-2-22-222-2-122-2-211-1-111-12-22-2−2i2i−2i2i-1-11-1-1111−2i2i0000-11i−ii−iii−i−i33−3−333−3−3000000i3−i3i3−i300000000000000
χ442-2-22-222-2-122-2-211-1-111-12-22-2−2i2i−2i2i-1-11-1-1111−2i2i0000-11i−ii−iii−i−i−3−333−3−333000000−i3i3−i3i300000000000000
χ452-2-22-222-2-122-2-211-1-111-1-22-222i−2i2i−2i-1-1111-1-11−2i2i00001-1−ii−iiii−i−i33−3−3−3−333000000−i3i3i3−i300000000000000
χ462-2-22-222-2-122-2-211-1-111-1-22-222i−2i2i−2i-1-1111-1-11−2i2i00001-1−ii−iiii−i−i−3−33333−3−3000000i3−i3−i3i300000000000000
χ472-2-22-222-2-122-2-211-1-111-1-22-22−2i2i−2i2i-1-1111-1-112i−2i00001-1i−ii−i−i−iii33−3−3−3−333000000i3−i3−i3i300000000000000
χ482-2-22-222-2-122-2-211-1-111-1-22-22−2i2i−2i2i-1-1111-1-112i−2i00001-1i−ii−i−i−iii−3−33333−3−3000000−i3i3i3−i300000000000000
χ492-2-2-222-2222-22-2-222-2-22-200002-2-222-220000-2000000002-2-22000000000000000000000000000002i−2i0002i−2i
χ502-2-2-222-2222-22-2-222-2-22-200002-2-222-220000-2000000002-2-2200000000000000000000000000000−2i2i000−2i2i
χ512-2-2-222-2222-22-2-222-2-22-20000-222-22-220000-200000000-222-2000000000000000000000000000002i−2i000−2i2i
χ522-2-2-222-2222-22-2-222-2-22-20000-222-22-220000-200000000-222-200000000000000000000000000000−2i2i0002i−2i
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222-2-2-2-22000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022222222000000-2-20000000000000000000000000000000000000000
χ55444-4-44-4-44-444-44-44-44-4-400000000-4440000-4000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-24-4-44-22-22-22200004i4i−4i−4i-2220000-200000000−2i−2i2i2i000000000000000000000000000000000000
χ57444-4-44-4-4-24-4-44-22-22-2220000−4i−4i4i4i-2220000-2000000002i2i−2i−2i000000000000000000000000000000000000
χ58444-4-44-4-4-2-444-4-22-22-222000000002-2-200002000000000000−2i32i3−2i32i300000000000000000000000000000000
χ59444-4-44-4-4-2-444-4-22-22-222000000002-2-2000020000000000002i3−2i32i3−2i300000000000000000000000000000000
χ6044-444-4-4-44000044-4-4-4-44000000000000000000−2i22i2000000000000−2i22i2−2i22i20000000000000000000000000000
χ6144-444-4-4-44000044-4-4-4-440000000000000000002i2−2i20000000000002i2−2i22i2−2i20000000000000000000000000000
χ6244-444-4-4-4-20000-2-22222-200000000000−2i32i3−2i32i3000−2i22i2000000000000i2−i2i2−i26−66−6000000000000000000000000
χ6344-444-4-4-4-20000-2-22222-200000000000−2i32i3−2i32i30002i2−2i2000000000000−i2i2−i2i2−66−66000000000000000000000000
χ6444-444-4-4-4-20000-2-22222-2000000000002i3−2i32i3−2i3000−2i22i2000000000000i2−i2i2−i2−66−66000000000000000000000000
χ6544-444-4-4-4-20000-2-22222-2000000000002i3−2i32i3−2i30002i2−2i2000000000000−i2i2−i2i26−66−6000000000000000000000000
χ6644-4-4-4-444400004-4-44-44-400000000000000000000000000000000000000004i−4i0000000000000000000000
χ6744-4-4-4-444400004-4-44-44-40000000000000000000000000000000000000000−4i4i0000000000000000000000
χ684-444-4-4-4440000-4-4-4-44440000000000000000000022−220000000000000022−22−2222000000000000000000000000
χ694-444-4-4-4440000-4-4-4-444400000000000000000000−222200000000000000−222222−22000000000000000000000000
χ704-444-4-4-44-200002222-2-2-200000000000−2i32i32i3−2i30000022−220000000000i6−i6−i6i6−222−2000000000000000000000000
χ714-444-4-4-44-200002222-2-2-200000000000−2i32i32i3−2i300000−22220000000000−i6i6i6−i62−2−22000000000000000000000000
χ724-444-4-4-44-200002222-2-2-2000000000002i3−2i3−2i32i30000022−220000000000−i6i6i6−i6−222−2000000000000000000000000
χ734-444-4-4-44-200002222-2-2-2000000000002i3−2i3−2i32i300000−22220000000000i6−i6−i6i62−2−22000000000000000000000000
χ744-44-44-44-440000-44-444-4-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ754-44-44-44-440000-44-444-4-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ764-4-44-444-4-2-4-44422-2-222-24-4-44000022-2-2-222-20000002-20000000000000000000000000000000000000000
χ774-4-44-444-4-2-4-44422-2-222-2-444-4000022-222-2-2-2000000-220000000000000000000000000000000000000000
χ784-4-4-444-444-44-44-444-4-44-400000000-44-400004000000000000000000000000000000000000000000000000
χ794-4-4-444-44-24-44-42-2-222-2200004-4-44-22-20000200000000-222-2000000000000000000000000000000000000
χ804-4-4-444-44-24-44-42-2-222-220000-444-4-22-200002000000002-2-22000000000000000000000000000000000000
χ814-4-4-444-44-2-44-442-2-222-22000000002-220000-200000000000023−23−232300000000000000000000000000000000
χ824-4-4-444-44-2-44-442-2-222-22000000002-220000-2000000000000−232323−2300000000000000000000000000000000
χ8388-8-8-8-888-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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