Finite Group Databasebeta

← Group #10844584

Character table — Group #10844584

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order12222222344446666666441212121222444448888121212122424242424242424444444444426666121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-1111111-1
χ511111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111111-1-111-1-1-1-1-1
χ611111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111111
χ711111111111111111111111111-1-11-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ811111111111111111111111111-1-11-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111111-111-1-1-1-111-111-1-111-1-1-1
χ1011111111111111111111-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1111
χ1111111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-111-1-111-1-1-11111-1-111-1
χ1211111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-111-1-11-1-1-1-111-1-11
χ1311111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111111-1-111-1-111-1-1-1-1-1-1-1111
χ1411111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-111-1-1111111111-1-1-1
χ1511111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-11111-1-1-1-1-11111-1-11
χ1611111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-11111-1-1111-1-1-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-20000000022220000-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-200000000-2-2-2-20000220000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-2220000000022-2-20000-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-22200000000-2-222000022000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-100000000002-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-11111111100000000002-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-222222-2-2-2-2-1-1-1-1111111110000000000-21111-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-222-2-222-2-21111-1-1-1-111110000000000-2-1-11111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-222-2-22211111111-1-1-1-10000000000-2-1-111-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-2-2-22211111111-1-1-1-10000000000211-1-111-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22222-2-21111-1-1-1-111110000000000211-1-1-1-1110000000000
χ2922-2-22-22-222-2-2222-22-2-2-2002-22-200000002i−2i0000002i2i−2i−2i0000000022-2-20000000000002i−2i0000000
χ3022-2-22-22-222-2-2222-22-2-2-2002-22-200000002i−2i0000002i2i−2i−2i00000000-2-222000000000000−2i2i0000000
χ3122-2-22-22-222-2-2222-22-2-2-2002-22-20000000−2i2i000000−2i−2i2i2i0000000022-2-2000000000000−2i2i0000000
χ3222-2-22-22-222-2-2222-22-2-2-2002-22-20000000−2i2i000000−2i−2i2i2i00000000-2-2220000000000002i−2i0000000
χ332-22-2-2-222222-2-2-2-222-22-20022-2-20002i−2i0000000000000000002-2002i−2i2i−2i2-200000002i−2i0000000000
χ342-22-2-2-222222-2-2-2-222-22-20022-2-20002i−2i000000000000000000-2200−2i2i−2i2i-2200000002i−2i0000000000
χ352-22-2-2-222222-2-2-2-222-22-20022-2-2000−2i2i0000000000000000002-200−2i2i−2i2i2-20000000−2i2i0000000000
χ362-22-2-2-222222-2-2-2-222-22-20022-2-2000−2i2i000000000000000000-22002i−2i2i−2i-220000000−2i2i0000000000
χ372-22-2-2-2222-2-222-2-222-22-200-2-222000002-200000000000000002-2000000-22000002-2000002-200000
χ382-22-2-2-2222-2-222-2-222-22-200-2-222000002-20000000000000000-220000002-2000002-200000-2200000
χ392-22-2-2-2222-2-222-2-222-22-200-2-22200000-2200000000000000002-2000000-2200000-2200000-2200000
χ402-22-2-2-2222-2-222-2-222-22-200-2-22200000-220000000000000000-220000002-200000-22000002-200000
χ412-2-22-222-222-22-2-2-2-222-22002-2-222-200000000000000000000000002i−2i−2i2i0002-2000000000002i−2i000
χ422-2-22-222-222-22-2-2-2-222-22002-2-222-20000000000000000000000000−2i2i2i−2i0002-200000000000−2i2i000
χ432-2-22-222-222-22-2-2-2-222-22002-2-22-2200000000000000000000000002i−2i−2i2i000-2200000000000−2i2i000
χ442-2-22-222-222-22-2-2-2-222-22002-2-22-220000000000000000000000000−2i2i2i−2i000-22000000000002i−2i000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244222200-400000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220040000000022-2-20000000000000000000000000000000000000
χ474444-4-4-4-4400004-44-44-4-44-40000000000000004-4000000000000000000000000000000000000000
χ484444-4-4-4-4400004-44-44-4-4-44000000000000000-44000000000000000000000000000000000000000
χ494444-4-4-4-4-20000-22-22-2224-4000000000000000-22006−66−666−6−600000000000000000000000000000
χ504444-4-4-4-4-20000-22-22-2224-4000000000000000-2200−66−66−6−66600000000000000000000000000000
χ514444-4-4-4-4-20000-22-22-222-440000000000000002-2006−66−6−6−66600000000000000000000000000000
χ524444-4-4-4-4-20000-22-22-222-440000000000000002-200−66−6666−6−600000000000000000000000000000
χ5344-4-44-44-44-444-444-44-4-4-400-44-440000000000000000000000000000000000000000000000000000
χ5444-4-44-44-4-24-4-44-2-22-222200-22-2200000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ5544-4-44-44-4-24-4-44-2-22-222200-22-220000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ5644-4-44-44-4-2-444-4-2-22-2222002-22-2000000000000000000023−2323−2300000000000000000000000000000
χ5744-4-44-44-4-2-444-4-2-22-2222002-22-20000000000000000000−2323−232300000000000000000000000000000
χ5844-4-4-44-44400004-4-4-4-44400000000000000022−220000000022−22−222200000000000000000000000000000
χ5944-4-4-44-44400004-4-4-4-444000000000000000−222200000000−222222−2200000000000000000000000000000
χ6044-4-4-44-44-20000-22222-2-200000000000000022−2200−2i32i3i6−i6−i6i6−222−200000000000000000000000000000
χ6144-4-4-44-44-20000-22222-2-200000000000000022−22002i3−2i3−i6i6i6−i6−222−200000000000000000000000000000
χ6244-4-4-44-44-20000-22222-2-2000000000000000−222200−2i32i3−i6i6i6−i62−2−2200000000000000000000000000000
χ6344-4-4-44-44-20000-22222-2-2000000000000000−2222002i3−2i3i6−i6−i6i62−2−2200000000000000000000000000000
χ644-44-444-4-440000-444-4-4-4400000000000000000000000000000004i−4i0000000000000000000000000
χ654-44-444-4-440000-444-4-4-440000000000000000000000000000000−4i4i0000000000000000000000000
χ664-44-4-4-444-244-4-422-2-22-2200-2-2220004i−4i00000000000000000000000000000000000−2i2i0000000000
χ674-44-4-4-444-244-4-422-2-22-2200-2-222000−4i4i000000000000000000000000000000000002i−2i0000000000
χ684-44-4-4-444-2-4-44422-2-22-220022-2-2000004-40000000000000000000000000000000-22000000000000
χ694-44-4-4-444-2-4-44422-2-22-220022-2-200000-4400000000000000000000000000000002-2000000000000
χ704-4-444-4-4440000-44-4-444-4000000000000000000000000000000000000000000000000000000022−220
χ714-4-444-4-4440000-44-4-444-40000000000000000000000000000000000000000000000000000000−22220
χ724-4-44-444-44-44-44-4-4-444-4400-444-40000000000000000000000000000000000000000000000000000
χ734-4-44-444-4-24-44-4222-2-22-200-222-24-400000000000000000000000000000000-220000000000000000
χ744-4-44-444-4-24-44-4222-2-22-200-222-2-44000000000000000000000000000000002-20000000000000000
χ754-4-44-444-4-2-44-44222-2-22-2002-2-22000000000000000000000000000000000000−2i32i300000000000000
χ764-4-44-444-4-2-44-44222-2-22-2002-2-220000000000000000000000000000000000002i3−2i300000000000000
χ778-88-888-8-8-400004-4-4444-40000000000000000000000000000000000000000000000000000000000
χ788-8-888-8-88-400004-444-4-440000000000000000000000000000000000000000000000000000000000

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