Finite Group Databasebeta

← Group #10855139

Character table — Group #10855139

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212244444488882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-111-1-111-1-111-1
χ1011111111111111111111-1-1111111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-111-1-11
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111-1-1-111-1-1-1-111-1-11
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1111111-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-1-111-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-11111-1-1-1
χ17222222222-2-2-2-22222222220000-2-22222-2-2-200000000-2-2000000000000000022-2-22200000-200000000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-200000000-2-20000000000000000-2-222-2-200000200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000000022000000000000000022-2-2-2-200000200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-2222200000-200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-222-2-222111111-1-1-1-1-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-222-2-2111111-1-1-1-11111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2222222-2-211-1-1-1-111111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-2-2-22211-1-1-1-11111-1-1-1-111110000002-1-111000000000000
χ2922-22-22-2-22-22-222-22-22-2-2002i2i−2i−2i-2-20000220000000000000002i2i−2i−2i0000000000000000000000002i−2i002-20
χ3022-22-22-2-22-22-222-22-22-2-2002i2i−2i−2i-2-20000220000000000000002i2i−2i−2i000000000000000000000000−2i2i00-220
χ3122-22-22-2-22-22-222-22-22-2-200−2i−2i2i2i-2-2000022000000000000000−2i−2i2i2i0000000000000000000000002i−2i00-220
χ3222-22-22-2-22-22-222-22-22-2-200−2i−2i2i2i-2-2000022000000000000000−2i−2i2i2i000000000000000000000000−2i2i002-20
χ332-22-222-2-222-2-22-2-222-22-2002i−2i2i−2i2-200002-20000000000000002i−2i2i−2i000000002-22-2000000002i−2i000000000
χ342-22-222-2-222-2-22-2-222-22-2002i−2i2i−2i2-200002-20000000000000002i−2i2i−2i00000000-22-2200000000−2i2i000000000
χ352-22-222-2-222-2-22-2-222-22-200−2i2i−2i2i2-200002-2000000000000000−2i2i−2i2i000000002-22-200000000−2i2i000000000
χ362-22-222-2-222-2-22-2-222-22-200−2i2i−2i2i2-200002-2000000000000000−2i2i−2i2i00000000-22-22000000002i−2i000000000
χ372-22-222-2-22-222-2-2-222-22-2000000-220000-2202i−2i000000002i2i−2i−2i0000000000002-2-2200000000002i−2i0000000
χ382-22-222-2-22-222-2-2-222-22-2000000-220000-2202i−2i000000002i2i−2i−2i000000000000-222-20000000000−2i2i0000000
χ392-22-222-2-22-222-2-2-222-22-2000000-220000-220−2i2i00000000−2i−2i2i2i0000000000002-2-220000000000−2i2i0000000
χ402-22-222-2-22-222-2-2-222-22-2000000-220000-220−2i2i00000000−2i−2i2i2i000000000000-222-200000000002i−2i0000000
χ412-2-2-2-22222-2-222-222-2-2-22002-2-22-2200002-20002-2002-20000002-2-2222-2-200000000000002-2000000000000
χ422-2-2-2-22222-2-222-222-2-2-22002-2-22-2200002-2000-2200-220000002-2-22-2-2220000000000000-22000000000000
χ432-2-2-2-22222-2-222-222-2-2-2200-222-2-2200002-20002-200-22000000-222-2-2-22200000000000002-2000000000000
χ442-2-2-2-22222-2-222-222-2-2-2200-222-2-2200002-2000-22002-2000000-222-222-2-20000000000000-22000000000000
χ452-2-2-2-2222-1-2-2221-1-1111-1002-2-221-133−3−3-110002-2002-23−33−33−3-111-1-1-11133−3−300000003−3-11000000000000
χ462-2-2-2-2222-1-2-2221-1-1111-1002-2-221-133−3−3-11000-2200-223−33−33−3-111-111-1-1−3−3330000000−331-1000000000000
χ472-2-2-2-2222-1-2-2221-1-1111-1002-2-221-1−3−333-110002-2002-2−33−33−33-111-1-1-111−3−3330000000−33-11000000000000
χ482-2-2-2-2222-1-2-2221-1-1111-1002-2-221-1−3−333-11000-2200-22−33−33−33-111-111-1-133−3−300000003−31-1000000000000
χ492-2-2-2-2222-1-2-2221-1-1111-100-222-21-133−3−3-110002-200-223−3−33−331-1-1111-1-1−3−33300000003−3-11000000000000
χ502-2-2-2-2222-1-2-2221-1-1111-100-222-21-133−3−3-11000-22002-23−3−33−331-1-11-1-11133−3−30000000−331-1000000000000
χ512-2-2-2-2222-1-2-2221-1-1111-100-222-21-1−3−333-110002-200-22−333−33−31-1-1111-1-133−3−30000000−33-11000000000000
χ522-2-2-2-2222-1-2-2221-1-1111-100-222-21-1−3−333-11000-22002-2−333−33−31-1-11-1-111−3−33300000003−31-1000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-222-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-4-44-4400004-4-44-4-444i−4i0000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ56444-4-4-44-4400004-4-44-4-44−4i4i000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ57444-4-4-44-4-20000-222-222-24i−4i000000−2i2i−2i2i000000000000000000000i6−i6i6−i66−66−600000000000000000000000
χ58444-4-4-44-4-20000-222-222-24i−4i000000−2i2i−2i2i000000000000000000000−i6i6−i6i6−66−6600000000000000000000000
χ59444-4-4-44-4-20000-222-222-2−4i4i0000002i−2i2i−2i000000000000000000000i6−i6i6−i6−66−6600000000000000000000000
χ60444-4-4-44-4-20000-222-222-2−4i4i0000002i−2i2i−2i000000000000000000000−i6i6−i6i66−66−600000000000000000000000
χ6144-44-44-4-444-44-44-44-44-4-4000000440000-4-400000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-24-44-4-22-22-222000000-2-200002200000000000−2i32i32i3−2i300000000000000000000000000000000000
χ6344-44-44-4-4-24-44-4-22-22-222000000-2-2000022000000000002i3−2i3−2i32i300000000000000000000000000000000000
χ6444-44-44-4-4-2-44-44-22-22-222004i4i−4i−4i220000-2-2000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6544-44-44-4-4-2-44-44-22-22-22200−4i−4i4i4i220000-2-20000000000000002i2i−2i−2i0000000000000000000000000000000
χ6644-4-44-4-444000044-4-4-44-400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ6744-4-44-4-444000044-4-4-44-4000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ684-444-4-4-4440000-44-444-4-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ694-444-4-4-4440000-44-444-4-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ704-44-444-4-4-24-4-4422-2-22-22004i−4i4i−4i-220000-22000000000000000−2i2i−2i2i0000000000000000000000000000000
χ714-44-444-4-4-24-4-4422-2-22-2200−4i4i−4i4i-220000-220000000000000002i−2i2i−2i0000000000000000000000000000000
χ724-44-444-4-4-2-444-422-2-22-220000002-200002-204i−4i00000000−2i−2i2i2i00000000000000000000000000000000000
χ734-44-444-4-4-2-444-422-2-22-220000002-200002-20−4i4i000000002i2i−2i−2i00000000000000000000000000000000000
χ744-4-444-44-440000-4-4-4-4444000000000000000000022−22000000000000000022−22−222200000000000000000000000
χ754-4-444-44-440000-4-4-4-44440000000000000000000−22220000000000000000−222222−2200000000000000000000000
χ764-4-444-44-4-200002222-2-2-200000000−2i32i32i3−2i3000000022−22000000000000i6−i6−i6i6−222−200000000000000000000000
χ774-4-444-44-4-200002222-2-2-200000000−2i32i32i3−2i30000000−2222000000000000−i6i6i6−i62−2−2200000000000000000000000
χ784-4-444-44-4-200002222-2-2-2000000002i3−2i3−2i32i3000000022−22000000000000−i6i6i6−i6−222−200000000000000000000000
χ794-4-444-44-4-200002222-2-2-2000000002i3−2i3−2i32i30000000−2222000000000000i6−i6−i6i62−2−2200000000000000000000000
χ804-4-4-4-4444444-4-4-444-4-4-440000004-40000-4400000000000000000000000000000000000000000000000000
χ814-4-4-4-4444-244-4-42-2-2222-2000000-222323−23−232-2000000000−2323000000000000000000000000000000000000000
χ824-4-4-4-4444-244-4-42-2-2222-2000000-22−23−2323232-200000000023−23000000000000000000000000000000000000000
χ8388-8-88-8-88-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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