Finite Group Databasebeta

← Group #10833378

Character table — Group #10833378

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order122222223444444666222444666666661212121212121212121222444444446666612121212121212121212121212121212124444444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1111-1-1-11-1-11-1-1111111-1-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-111
χ61111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1111-1-1-11-1-11-1-1111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ911111-1-1111-1-1111111-111-11111-1-111111111-1-11111-11-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11-11-1
χ1011111-1-1111-1-1111111-111-11111-1-111111111-1-11111-11-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-11-11
χ1111111-1-1111-1-1111111-111-11111-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ1211111-1-1111-1-1111111-111-11111-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1
χ1311111-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-111-111-1
χ1411111-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ1511111-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-11-111-111-1-11111-1-1-1-1-111-1-111111111-1-1-1-1-1-1111-1-11
χ1611111-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-11-111-111-1-11111-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-111-1
χ17222222222-2-2-2-2-2-2222200-20022220000-2-2-2-2-2-2000000002-2002-220000000022-2-2-2000022-2-20000000000000000
χ18222222222-2-2-2-2-2-2222200-20022220000-2-2-2-2-2-200000000-2200-22200000000-2-222-20000-2-2220000000000000000
χ1922222222-1222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2022222222-1222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-22-2-2-2-1-1-11111111111-1-1-11111110000000000000000
χ2122222222-1222222-1-1-12-2-22-2-2-1-1-1-11111-1-1-1-1-1-11111-2222-2-2-22-2-2-111-1-1-1-1-1-11111-111-1-111110000000000000000
χ2222222222-1222222-1-1-12-2-22-2-2-1-1-1-11111-1-1-1-1-1-11111-2-2-2-222-2-222-111111111-1-1-1-1-11111-1-1-1-10000000000000000
χ2322222222-1-2-2-2-2-2-2-1-1-1200-200-1-1-1-1−i3−i3i3i3111111−i3−i3i3i300002-2002-2-1−i3i3−i3i3−i3i3−i3i3-1-1111−i3i3−i3i3-1-1110000000000000000
χ2422222222-1-2-2-2-2-2-2-1-1-1200-200-1-1-1-1−i3−i3i3i3111111−i3−i3i3i30000-2200-22-1−i3i3i3−i3i3−i3i3−i311-1-11−i3i3i3−i311-1-10000000000000000
χ2522222222-1-2-2-2-2-2-2-1-1-1200-200-1-1-1-1i3i3−i3−i3111111i3i3−i3−i300002-2002-2-1i3−i3i3−i3i3−i3i3−i3-1-1111i3−i3i3−i3-1-1110000000000000000
χ2622222222-1-2-2-2-2-2-2-1-1-1200-200-1-1-1-1i3i3−i3−i3111111i3i3−i3−i30000-2200-22-1i3−i3−i3i3−i3i3−i3i311-1-11i3−i3−i3i311-1-10000000000000000
χ2722222-2-222-222-2-2-2222-20020022-2-20000-2-2-2-222000000002-200-22-20000000022-2-220000-2-2220000000000000000
χ2822222-2-222-222-2-2-2222-20020022-2-20000-2-2-2-22200000000-22002-2-200000000-2-2222000022-2-20000000000000000
χ2922222-2-22-12-2-2222-1-1-1-222-222-1-111-1-1-1-1-1-1-1-111-1-1-1-1-22-2-2-2-2-2222111-1-111111111111-1-1-1-1-1-10000000000000000
χ3022222-2-22-12-2-2222-1-1-1-222-222-1-111-1-1-1-1-1-1-1-111-1-1-1-1-2-22222-2-2-2-211111-1-1-1-1-1-1-1-11111111110000000000000000
χ3122222-2-22-12-2-2222-1-1-1-2-2-2-2-2-2-1-1111111-1-1-1-111111122-2-22222-2-21-1-1-1-11111-1-1-1-11-1-1-1-111110000000000000000
χ3222222-2-22-12-2-2222-1-1-1-2-2-2-2-2-2-1-1111111-1-1-1-11111112-222-2-22-2221-1-111-1-1-1-111111-1-111-1-1-1-10000000000000000
χ3322222-2-22-1-222-2-2-2-1-1-1-200200-1-111−i3−i3i3i31111-1-1−i3−i3i3i300002-200-221i3−i3i3−i3−i3i3−i3i3-1-111-1i3−i3i3−i311-1-10000000000000000
χ3422222-2-22-1-222-2-2-2-1-1-1-200200-1-111−i3−i3i3i31111-1-1−i3−i3i3i30000-22002-21i3−i3−i3i3i3−i3i3−i311-1-1-1i3−i3−i3i3-1-1110000000000000000
χ3522222-2-22-1-222-2-2-2-1-1-1-200200-1-111i3i3−i3−i31111-1-1i3i3−i3−i300002-200-221−i3i3−i3i3i3−i3i3−i3-1-111-1−i3i3−i3i311-1-10000000000000000
χ3622222-2-22-1-222-2-2-2-1-1-1-200200-1-111i3i3−i3−i31111-1-1i3i3−i3−i30000-22002-21−i3i3i3−i3−i3i3−i3i311-1-1-1−i3i3i3−i3-1-1110000000000000000
χ372222-222-22222-2-22222-200-200-2-222000022-2-2220000022-2000-200-2002222-2-20000-200-2-200000000000000000000
χ382222-222-22222-2-22222-200-200-2-222000022-2-22200000-2-22000200-200-2-2-2-2220000-2002200000000000000000000
χ392222-222-22-2-2-222-2222-2222-2-2-2-2222222-2-222-2-2-2-2-2-2200000-2000-22200000000002-2-20000000000000000000000
χ402222-222-22-2-2-222-2222-2-2-2222-2-222-2-2-2-2-2-222-2-22222-2000002000-2-2-200000000002220000000000000000000000
χ412222-222-2-1222-2-22-1-1-1-200-20011-1-1−i3−i3i3i3-1-111-1-1i3i3−i3−i3022-2000-2001−i3i3-1-1-1-111−i3i3−i3i31i3−i311−i3i3−i3i30000000000000000
χ422222-222-2-1222-2-22-1-1-1-200-20011-1-1−i3−i3i3i3-1-111-1-1i3i3−i3−i30-2-220002001−i3i31111-1-1i3−i3i3−i31i3−i3-1-1i3−i3i3−i30000000000000000
χ432222-222-2-1222-2-22-1-1-1-200-20011-1-1i3i3−i3−i3-1-111-1-1−i3−i3i3i3022-2000-2001i3−i3-1-1-1-111i3−i3i3−i31−i3i311i3−i3i3−i30000000000000000
χ442222-222-2-1222-2-22-1-1-1-200-20011-1-1i3i3−i3−i3-1-111-1-1−i3−i3i3i30-2-220002001i3−i31111-1-1−i3i3−i3i31−i3i3-1-1−i3i3−i3i30000000000000000
χ452222-222-2-1-2-2-222-2-1-1-1-2222-2-211-1-1-1-1-1-111-1-1111111200000-20001-1-1−i3i3−i3i3i3−i3−i3i3i3−i3-111i3−i3−i3i3i3−i30000000000000000
χ462222-222-2-1-2-2-222-2-1-1-1-2222-2-211-1-1-1-1-1-111-1-1111111200000-20001-1-1i3−i3i3−i3−i3i3i3−i3−i3i3-111−i3i3i3−i3−i3i30000000000000000
χ472222-222-2-1-2-2-222-2-1-1-1-2-2-222211-1-1111111-1-111-1-1-1-1-2000002000111−i3i3−i3i3i3−i3i3−i3−i3i3-1-1-1i3−i3i3−i3−i3i30000000000000000
χ482222-222-2-1-2-2-222-2-1-1-1-2-2-222211-1-1111111-1-111-1-1-1-1-2000002000111i3−i3i3−i3−i3i3−i3i3i3−i3-1-1-1−i3i3−i3i3i3−i30000000000000000
χ492222-2-2-2-222-2-2-2-22222200200-2-2-2-2000022-2-2-2-2000002-22000-20020022-2-2220000200-2-200000000000000000000
χ502222-2-2-2-222-2-2-2-22222200200-2-2-2-2000022-2-2-2-200000-22-2000200200-2-222-2-200002002200000000000000000000
χ512222-2-2-2-22-22222-2222222-2-2-2-2-2-2-22222-2-22222-2-2-2-2-20000020002-2-20000000000-2220000000000000000000000
χ522222-2-2-2-22-22222-22222-2-2-222-2-2-2-2-2-2-2-2-2-222222222200000-20002220000000000-2-2-20000000000000000000000
χ532222-2-2-2-2-12-2-2-2-22-1-1-12002001111−i3−i3i3i3-1-11111i3i3−i3−i302-22000-200-1i3−i3-1-111-1-1i3−i3i3−i3-1−i3i311−i3i3−i3i30000000000000000
χ542222-2-2-2-2-12-2-2-2-22-1-1-12002001111−i3−i3i3i3-1-11111i3i3−i3−i30-22-2000200-1i3−i311-1-111−i3i3−i3i3-1−i3i3-1-1i3−i3i3−i30000000000000000
χ552222-2-2-2-2-12-2-2-2-22-1-1-12002001111i3i3−i3−i3-1-11111−i3−i3i3i302-22000-200-1−i3i3-1-111-1-1−i3i3−i3i3-1i3−i311i3−i3i3−i30000000000000000
χ562222-2-2-2-2-12-2-2-2-22-1-1-12002001111i3i3−i3−i3-1-11111−i3−i3i3i30-22-2000200-1−i3i311-1-111i3−i3i3−i3-1i3−i3-1-1−i3i3−i3i30000000000000000
χ572222-2-2-2-2-1-22222-2-1-1-1222-2-2-21111-1-1-1-111-1-1-1-11111-2000002000-111−i3i3i3−i3−i3i3i3−i3−i3i31-1-1i3−i3−i3i3i3−i30000000000000000
χ582222-2-2-2-2-1-22222-2-1-1-1222-2-2-21111-1-1-1-111-1-1-1-11111-2000002000-111i3−i3−i3i3i3−i3−i3i3i3−i31-1-1−i3i3i3−i3−i3i30000000000000000
χ592222-2-2-2-2-1-22222-2-1-1-12-2-2-2221111111111-1-1-1-1-1-1-1-1200000-2000-1-1-1−i3i3i3−i3−i3i3−i3i3i3−i3111i3−i3i3−i3−i3i30000000000000000
χ602222-2-2-2-2-1-22222-2-1-1-12-2-2-2221111111111-1-1-1-1-1-1-1-1200000-2000-1-1-1i3−i3−i3i3i3−i3i3−i3−i3i3111−i3i3−i3i3i3−i30000000000000000
χ612-2-22200-222002-2-2-2-2202-202-22-2002-22-22-22-2002-22-2000000000000000000000000000000002i2i−2i−2i00002i−2i000000
χ622-2-22200-222002-2-2-2-2202-202-22-2002-22-22-22-2002-22-200000000000000000000000000000000−2i−2i2i2i0000−2i2i000000
χ632-2-22200-222002-2-2-2-220-220-222-200-22-222-22-200-22-22000000000000000000000000000000002i2i−2i−2i0000−2i2i000000
χ642-2-22200-222002-2-2-2-220-220-222-200-22-222-22-200-22-2200000000000000000000000000000000−2i−2i2i2i00002i−2i000000
χ652-2-22-20022-2002-22-2-2202-20-22-22002-22-2-222-200-22-2200000000000000000000000000000000000022-2-2002-20000
χ662-2-22-20022-2002-22-2-2202-20-22-22002-22-2-222-200-22-22000000000000000000000000000000000000-2-22200-220000
χ672-2-22-20022-2002-22-2-220-2202-2-2200-22-22-222-2002-22-200000000000000000000000000000000000022-2-200-220000
χ682-2-22-20022-2002-22-2-220-2202-2-2200-22-22-222-2002-22-2000000000000000000000000000000000000-2-222002-20000
χ6944-4-404-4040000004-4-4000000004-400000000000000000000000000000000000000000000002-22-22-22-200000000
χ7044-4-404-4040000004-4-4000000004-40000000000000000000000000000000000000000000000-22-22-22-2200000000
χ7144-4-40-44040000004-4-400000000-4400000000000000000000000000000000000000000000002-22-2-22-2200000000
χ7244-4-40-44040000004-4-400000000-440000000000000000000000000000000000000000000000-22-222-22-200000000
χ734-44-40000404i−4i000-44-40000000000000000004i−4i0000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ744-44-40000404i−4i000-44-40000000000000000004i−4i000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ754-44-4000040−4i4i000-44-4000000000000000000−4i4i0000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ764-44-4000040−4i4i000-44-4000000000000000000−4i4i000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ774-4-44400-44-400-444-4-440000004-4000000-44-44000000000000000000000000000000000000000000000000000000
χ784-4-44400-4-24004-4-422-204-404-4-2200-22-22-22-2200-22-22000000000000000000000000000000000000000000000000
χ794-4-44400-4-24004-4-422-20-440-44-22002-22-2-22-22002-22-2000000000000000000000000000000000000000000000000
χ804-4-44400-4-2-400-44422-2000000-2200−2i32i32i3−2i32-22-200−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ814-4-44400-4-2-400-44422-2000000-22002i3−2i3−2i32i32-22-2002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ824-4-44-40044400-44-4-4-44000000-440000004-4-44000000000000000000000000000000000000000000000000000000
χ834-4-44-4004-2400-44-422-20000002-200−2i32i32i3−2i3-222-2002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ844-4-44-4004-2400-44-422-20000002-2002i3−2i3−2i32i3-222-200−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ854-4-44-4004-2-4004-4422-204-40-442-200-22-222-2-22002-22-2000000000000000000000000000000000000000000000000
χ864-4-44-4004-2-4004-4422-20-4404-42-2002-22-22-2-2200-22-22000000000000000000000000000000000000000000000000
χ8788-8-808-80-4000000-44400000000-4400000000000000000000000000000000000000000000000000000000000000
χ8888-8-80-880-4000000-444000000004-400000000000000000000000000000000000000000000000000000000000000
χ898-88-80000-408i−8i0004-44000000000000000000−4i4i0000000000000000000000000000000000000000000000000000
χ908-88-80000-40−8i8i0004-440000000000000000004i−4i0000000000000000000000000000000000000000000000000000

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