Finite Group Databasebeta

← Group #10845240

Character table — Group #10845240

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
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111
χ61111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-1-1
χ71111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1111-1-1111-1-1-1-1
χ81111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-11111
χ911111111111111111111-1-11111-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-111-1-1-1-111-1111-1-111-1-1
χ1011111111111111111111-1-11111-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-1-111-1-11-1-1-111-1-111
χ1111111111111111111111-1-11111-1-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-1-1-1-111111-1-111
χ1211111111111111111111-1-11111-1-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-11111111-1-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-11-1-11111-1-1-1-1-111111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-11-1-111-1-111111-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-11-111-1-11111-1-1-11-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1111-111-1-1-1-1-1-1111-11111-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2-22222-200000000000000-2-20000000022220000000000-200-2000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-22222-200000000000000-2-200000000-2-2-2-200000000002002000000
χ19222222222-2-2-2-22222222-2-2000022-2-2-2-2-2-2-2-200000000000000220000000022-2-20000000000200-2000000
χ20222222222-2-2-2-22222222-2-2000022-2-2-2-2-2-2-2-2000000000000002200000000-2-2220000000000-2002000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-2-2222211111111-1-1-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111-1-111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-11111-1-2-222-2-2-1-1-1-1111111-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-11111-1-2-2-2-222-1-1-1-11111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-12222-2-21111-1-1-1-111-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-2-2221111-1-1-1-1111111-1-1-1-100002-2-1-11100000000000000
χ2922-22-22-2-222-2-222-22-22-2-2002i2i−2i−2i002-2-2000020000002i2i−2i−2i000000000000000000000000002-20000002i−2i00
χ3022-22-22-2-222-2-222-22-22-2-2002i2i−2i−2i002-2-2000020000002i2i−2i−2i00000000000000000000000000-22000000−2i2i00
χ3122-22-22-2-222-2-222-22-22-2-200−2i−2i2i2i002-2-200002000000−2i−2i2i2i000000000000000000000000002-2000000−2i2i00
χ3222-22-22-2-222-2-222-22-22-2-200−2i−2i2i2i002-2-200002000000−2i−2i2i2i00000000000000000000000000-220000002i−2i00
χ332-22-2-22-22222-2-2-2-222-2-222-22i−2i2i−2i2-222-222-2-2-22i−2i00002i−2i2i−2i2i2i−2i−2i2-200000000000000000000000000000000
χ342-22-2-22-22222-2-2-2-222-2-222-2−2i2i−2i2i2-222-222-2-2-2−2i2i0000−2i2i−2i2i−2i−2i2i2i2-200000000000000000000000000000000
χ352-22-2-22-22222-2-2-2-222-2-22-222i−2i2i−2i-2222-2-2-222-2−2i2i00002i−2i2i−2i−2i−2i2i2i-2200000000000000000000000000000000
χ362-22-2-22-22222-2-2-2-222-2-22-22−2i2i−2i2i-2222-2-2-222-22i−2i0000−2i2i−2i2i2i2i−2i−2i-2200000000000000000000000000000000
χ372-22-2-22-222-2-222-2-222-2-222-20000-22-2-2222-2-2200000000000000-220000000000000000002-20002-20000000
χ382-22-2-22-222-2-222-2-222-2-222-20000-22-2-2222-2-2200000000000000-22000000000000000000-22000-220000000
χ392-22-2-22-222-2-222-2-222-2-22-2200002-2-2-22-2-2222000000000000002-20000000000000000002-2000-220000000
χ402-22-2-22-222-2-222-2-222-2-22-2200002-2-2-22-2-2222000000000000002-2000000000000000000-220002-20000000
χ412-22-2-22-22-122-2-211-1-111-12-22i−2i2i−2i2-2-1-11-1-11112i−2i0000−ii−ii−i−iii-1133−3−333−3−3000000−i3i3−i3i300000000000000
χ422-22-2-22-22-122-2-211-1-111-12-22i−2i2i−2i2-2-1-11-1-11112i−2i0000−ii−ii−i−iii-11−3−333−3−333000000i3−i3i3−i300000000000000
χ432-22-2-22-22-122-2-211-1-111-12-2−2i2i−2i2i2-2-1-11-1-1111−2i2i0000i−ii−iii−i−i-1133−3−333−3−3000000i3−i3i3−i300000000000000
χ442-22-2-22-22-122-2-211-1-111-12-2−2i2i−2i2i2-2-1-11-1-1111−2i2i0000i−ii−iii−i−i-11−3−333−3−333000000−i3i3−i3i300000000000000
χ452-22-2-22-22-122-2-211-1-111-1-222i−2i2i−2i-22-1-1111-1-11−2i2i0000−ii−iiii−i−i1-133−3−3−3−333000000−i3i3i3−i300000000000000
χ462-22-2-22-22-122-2-211-1-111-1-222i−2i2i−2i-22-1-1111-1-11−2i2i0000−ii−iiii−i−i1-1−3−33333−3−3000000i3−i3−i3i300000000000000
χ472-22-2-22-22-122-2-211-1-111-1-22−2i2i−2i2i-22-1-1111-1-112i−2i0000i−ii−i−i−iii1-133−3−3−3−333000000i3−i3−i3i300000000000000
χ482-22-2-22-22-122-2-211-1-111-1-22−2i2i−2i2i-22-1-1111-1-112i−2i0000i−ii−i−i−iii1-1−3−33333−3−3000000−i3i3i3−i300000000000000
χ492-2-2-2222-222-22-2-222-2-22-2002-2-22002-220000-20000002-2-22000000000000000000000000000000002i−2i002i−2i
χ502-2-2-2222-222-22-2-222-2-22-2002-2-22002-220000-20000002-2-2200000000000000000000000000000000−2i2i00−2i2i
χ512-2-2-2222-222-22-2-222-2-22-200-222-2002-220000-2000000-222-2000000000000000000000000000000002i−2i00−2i2i
χ522-2-2-2222-222-22-2-222-2-22-200-222-2002-220000-2000000-222-200000000000000000000000000000000−2i2i002i−2i
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-4-4222-2-2-2-22000000000000002200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000442222222200000000000000-2-200000000000000000000000000000000
χ55444-44-4-4-44000044-44-4-4-40000000000000000000022−220000000000000022−2222−22000000000000000000000000
χ56444-44-4-4-44000044-44-4-4-400000000000000000000−222200000000000000−2222−2222000000000000000000000000
χ57444-44-4-4-4-20000-2-22-222200000000000−2i32i3−2i32i30000022−220000000000i6−i6i6−i6−22−22000000000000000000000000
χ58444-44-4-4-4-20000-2-22-222200000000000−2i32i3−2i32i300000−22220000000000−i6i6−i6i62−22−2000000000000000000000000
χ59444-44-4-4-4-20000-2-22-2222000000000002i3−2i32i3−2i30000022−220000000000−i6i6−i6i6−22−22000000000000000000000000
χ60444-44-4-4-4-20000-2-22-2222000000000002i3−2i32i3−2i300000−22220000000000i6−i6i6−i62−22−2000000000000000000000000
χ6144-44-44-4-44-444-44-44-44-4-400000000-4440000-4000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-24-4-44-22-22-222004i4i−4i−4i00-2220000-2000000−2i−2i2i2i00000000000000000000000000000000000000
χ6344-44-44-4-4-24-4-44-22-22-22200−4i−4i4i4i00-2220000-20000002i2i−2i−2i00000000000000000000000000000000000000
χ6444-44-44-4-4-2-444-4-22-22-222000000002-2-2000020000000000−2i32i3−2i32i30000000000000000000000000000000000
χ6544-44-44-4-4-2-444-4-22-22-222000000002-2-20000200000000002i3−2i32i3−2i30000000000000000000000000000000000
χ6644-4-4-4-444400004-4-4-4-4440000000000000000000000000000000000000000004-400000000000000000000
χ6744-4-4-4-444400004-4-4-4-444000000000000000000000000000000000000000000-4400000000000000000000
χ684-444-4-44-440000-4-4-4444-4000000000000000000−2i22i2000000000000−2i22i22i2−2i20000000000000000000000000000
χ694-444-4-44-440000-4-4-4444-40000000000000000002i2−2i20000000000002i2−2i2−2i22i20000000000000000000000000000
χ704-444-4-44-4-20000222-2-2-2200000000000−2i32i32i3−2i3000−2i22i2000000000000i2−i2−i2i26−6−66000000000000000000000000
χ714-444-4-44-4-20000222-2-2-2200000000000−2i32i32i3−2i30002i2−2i2000000000000−i2i2i2−i2−666−6000000000000000000000000
χ724-444-4-44-4-20000222-2-2-22000000000002i3−2i3−2i32i3000−2i22i2000000000000i2−i2−i2i2−666−6000000000000000000000000
χ734-444-4-44-4-20000222-2-2-22000000000002i3−2i3−2i32i30002i2−2i2000000000000−i2i2i2−i26−6−66000000000000000000000000
χ744-44-4-44-44-2-4-44422-2-222-24-40000-4422-2-2-222-2000000000000002-200000000000000000000000000000000
χ754-44-4-44-44-2-4-44422-2-222-2-4400004-422-222-2-2-200000000000000-2200000000000000000000000000000000
χ764-4-444-4-4440000-44-4-44-4400000000000000000000000000000000000000004-40000000000000000000000
χ774-4-444-4-4440000-44-4-44-440000000000000000000000000000000000000000-440000000000000000000000
χ784-4-4-4444-44-44-44-444-4-44-400000000-44-400004000000000000000000000000000000000000000000000000
χ794-4-4-4444-4-24-44-42-2-222-22004-4-4400-22-200002000000-222-200000000000000000000000000000000000000
χ804-4-4-4444-4-24-44-42-2-222-2200-444-400-22-2000020000002-2-2200000000000000000000000000000000000000
χ814-4-4-4444-4-2-44-442-2-222-22000000002-220000-2000000000023−23−23230000000000000000000000000000000000
χ824-4-4-4444-4-2-44-442-2-222-22000000002-220000-20000000000−232323−230000000000000000000000000000000000
χ8388-8-8-8-888-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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