Finite Group Databasebeta

← Group #10853218

Character table — Group #10853218

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order122222223444466666664412121212444444488881212121224242424242424242244444444412121212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-111-1-111-1-1-1-1111-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-111111
χ511111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111111-1-1-1-1-1-11
χ611111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1111111-1
χ711111111111111111111111111-1-11-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1
χ811111111111111111111111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1111111-111-1-1-1-11111-1-1-111-1-1-1
χ1011111111111111111111-1-1111111-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111-1-1111-1-1111
χ1111111111111111111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-1-1-11111111-1-1-1
χ1311111111111111111111-1-11111-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111111-111-1-111-1
χ1411111111111111111111-1-11111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-11111-1-11-1-111-1-11
χ1511111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11-1-11111-1-1-1-1-11111-1-11
χ1611111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111-1-11111-1-1111-1-1-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-20000000022-2-2-2-200000000000000020000000
χ18222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-200000000-2-22222000000000000000-20000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-222000000002222-2-2000000000000000-20000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-22200000000-2-2-2-22200000000000000020000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-2-2-2-2-1-1-1-1111111110000000000-2-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-222-2-2-2-2-1-1-1-1111111110000000000211-1-111-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-222-2-2221111-1-1-1-111110000000000-2-1-11111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-222-2-211111111-1-1-1-100000000002-1-1-1-111110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2222222-2-211111111-1-1-1-10000000000-21111-1-1-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-2-2-2221111-1-1-1-111110000000000211-1-1-1-1110000000000
χ2922-2-222-2-2222-2-22-2-222-2-20022-2-22-20000000000000000000002-2002-222-2-202-20000000000000000
χ3022-2-222-2-2222-2-22-2-222-2-20022-2-22-2000000000000000000000-2200-22-2-22202-20000000000000000
χ3122-2-222-2-2222-2-22-2-222-2-20022-2-2-220000000000000000000002-2002-2-2-2220-220000000000000000
χ3222-2-222-2-2222-2-22-2-222-2-20022-2-2-22000000000000000000000-2200-2222-2-20-220000000000000000
χ3322-2-222-2-22-2-2222-2-222-2-200-2-2220002i−2i0000000000000000002-200-220000000002i−2i000002i−2i00000
χ3422-2-222-2-22-2-2222-2-222-2-200-2-2220002i−2i000000000000000000-22002-20000000002i−2i00000−2i2i00000
χ3522-2-222-2-22-2-2222-2-222-2-200-2-222000−2i2i0000000000000000002-200-22000000000−2i2i00000−2i2i00000
χ3622-2-222-2-22-2-2222-2-222-2-200-2-222000−2i2i000000000000000000-22002-2000000000−2i2i000002i−2i00000
χ372-22-22-22-222-22-2-2-2-22-222002-22-2000002-200000000000000000000002i−2i2i−2i00000002-2000002i−2i000
χ382-22-22-22-222-22-2-2-2-22-222002-22-2000002-20000000000000000000000−2i2i−2i2i00000002-200000−2i2i000
χ392-22-22-22-222-22-2-2-2-22-222002-22-200000-2200000000000000000000002i−2i2i−2i0000000-2200000−2i2i000
χ402-22-22-22-222-22-2-2-2-22-222002-22-200000-220000000000000000000000−2i2i−2i2i0000000-22000002i−2i000
χ412-2-222-2-2222-2-22-2222-2-2-2002-2-220000000002-2000022-2-200000000002i−2i−2i2i0000000002i−2i00000000
χ422-2-222-2-2222-2-22-2222-2-2-2002-2-220000000002-2000022-2-20000000000−2i2i2i−2i000000000−2i2i00000000
χ432-2-222-2-2222-2-22-2222-2-2-2002-2-22000000000-220000-2-22200000000002i−2i−2i2i000000000−2i2i00000000
χ442-2-222-2-2222-2-22-2222-2-2-2002-2-22000000000-220000-2-2220000000000−2i2i2i−2i0000000002i−2i00000000
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
χ474444-4-4-4-440000-44-4-444-4000000000000022−2200000000002222−22−2200000000000000000000000000000
χ484444-4-4-4-440000-44-4-444-40000000000000−22220000000000−22−22222200000000000000000000000000000
χ494444-4-4-4-4-200002-222-2-22000000000000022−22000023−236−66−6−2−22200000000000000000000000000000
χ504444-4-4-4-4-200002-222-2-22000000000000022−220000−2323−66−66−2−22200000000000000000000000000000
χ514444-4-4-4-4-200002-222-2-220000000000000−2222000023−23−66−6622−2−200000000000000000000000000000
χ524444-4-4-4-4-200002-222-2-220000000000000−22220000−23236−66−622−2−200000000000000000000000000000
χ5344-4-444-4-4-244-4-4-222-2-22200-2-2224-400000000000000000000000000000000-220000000000000000
χ5444-4-444-4-4-244-4-4-222-2-22200-2-222-44000000000000000000000000000000002-20000000000000000
χ5544-4-444-4-4-2-4-444-222-2-2220022-2-20004i−4i000000000000000000000000000000000−2i2i000000000000
χ5644-4-444-4-4-2-4-444-222-2-2220022-2-2000−4i4i0000000000000000000000000000000002i−2i000000000000
χ5744-4-4-4-44440000-4-44-44-44000000000000000000000000000000000000000000000000000000022−220
χ5844-4-4-4-44440000-4-44-44-440000000000000000000000000000000000000000000000000000000−22220
χ594-44-44-44-44-44-44-4-4-44-44400-44-440000000000000000000000000000000000000000000000000000
χ604-44-44-44-4-24-44-4222-22-2-200-22-22000004-4000000000000000000000000000000000-220000000000
χ614-44-44-44-4-24-44-4222-22-2-200-22-2200000-440000000000000000000000000000000002-20000000000
χ624-44-44-44-4-2-44-44222-22-2-2002-22-2000000000000000000000000000000000000−2i32i300000000000000
χ634-44-44-44-4-2-44-44222-22-2-2002-22-20000000000000000000000000000000000002i3−2i300000000000000
χ644-44-4-44-44400004-44-4-44-400000000000000000000000000000004i−4i0000000000000000000000000
χ654-44-4-44-44400004-44-4-44-40000000000000000000000000000000−4i4i0000000000000000000000000
χ664-4-444-4-444-444-4-4444-4-4-400-444-40000000000000000000000000000000000000000000000000000
χ674-4-444-4-44-24-4-442-2-2-222200-222-20000000004-40000-2-222000000000000000000000000000000000
χ684-4-444-4-44-24-4-442-2-2-222200-222-2000000000-44000022-2-2000000000000000000000000000000000
χ694-4-444-4-44-2-444-42-2-2-2222002-2-220000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ704-4-444-4-44-2-444-42-2-2-2222002-2-2200000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ714-4-44-444-44000044-4-4-4-444i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ724-4-44-444-44000044-4-4-4-44−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ734-4-44-444-4-20000-2-22222-24i−4i000000000000000−2i2i006−6−66i6−i6−i6i600000000000000000000000000000
χ744-4-44-444-4-20000-2-22222-24i−4i000000000000000−2i2i00−666−6−i6i6i6−i600000000000000000000000000000
χ754-4-44-444-4-20000-2-22222-2−4i4i0000000000000002i−2i006−6−66−i6i6i6−i600000000000000000000000000000
χ764-4-44-444-4-20000-2-22222-2−4i4i0000000000000002i−2i00−666−6i6−i6−i6i600000000000000000000000000000
χ7788-8-8-8-888-4000044-44-44-40000000000000000000000000000000000000000000000000000000000
χ788-88-8-88-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000

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