Finite Group Databasebeta

← Group #10853233

Character table — Group #10853233

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
χ31111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11111-1-11-1-111-1-1-1-11
χ41111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-111-1-11111-1
χ511111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-111-1-1-1-111111-1-1-1-1-1-1-1
χ611111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11111111
χ711111111111111111111111111-1-1-1-11-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ811111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-11111-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1111-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-11111-1-111-1
χ1211111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1111-1-1-1-111-1-11
χ1311111111111111111111-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1111
χ1411111111111111111111-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-11111111-1-1-1
χ1511111111111111111111-1-11111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-1-1-11111-111-1-111-1-11
χ1611111111111111111111-1-11111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-111-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-20000000022-2-2000022000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-200000000-2-2220000-2-20000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-2220000000022-2-20000-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-22200000000-2-222000022000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122-2-22-2-2-2-2-2-2-1-1-1-1111111110000000000211-1-1-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-222222-2-2-2-2-1-1-1-1111111110000000000-2-1-11111-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-12222-2-2-2-2-2221111-1-1-1-111110000000000-2-1-1-1-111110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-22222-2-211111111-1-1-1-10000000000-211-1-111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-222-2-2-222-2-211111111-1-1-1-100000000002-1-111-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-222-2-2221111-1-1-1-11111000000000021111-1-1-1-10000000000
χ2922-222-2-2-2222-2-22-2-222-2-20022-2-2002-200000000000000000002-22-222-2-20002-20000000000000000
χ3022-222-2-2-2222-2-22-2-222-2-20022-2-2002-20000000000000000000-22-22-2-2220002-20000000000000000
χ3122-222-2-2-2222-2-22-2-222-2-20022-2-200-2200000000000000000002-22-2-2-222000-220000000000000000
χ3222-222-2-2-2222-2-22-2-222-2-20022-2-200-220000000000000000000-22-2222-2-2000-220000000000000000
χ3322-222-2-2-22-2-2222-2-222-2-200-2-222000002i−2i00000000000000002-2-2200000000000002i−2i02i−2i0000000
χ3422-222-2-2-22-2-2222-2-222-2-200-2-222000002i−2i0000000000000000-222-200000000000002i−2i0−2i2i0000000
χ3522-222-2-2-22-2-2222-2-222-2-200-2-22200000−2i2i00000000000000002-2-220000000000000−2i2i0−2i2i0000000
χ3622-222-2-2-22-2-2222-2-222-2-200-2-22200000−2i2i0000000000000000-222-20000000000000−2i2i02i−2i0000000
χ372-222-2-2-2222-22-2-2-2-22-222002-22-22-200000000000000000000000002i−2i2i−2i000002-20000000002i−2i000
χ382-222-2-2-2222-22-2-2-2-22-222002-22-22-20000000000000000000000000−2i2i−2i2i000002-2000000000−2i2i000
χ392-222-2-2-2222-22-2-2-2-22-222002-22-2-2200000000000000000000000002i−2i2i−2i00000-22000000000−2i2i000
χ402-222-2-2-2222-22-2-2-2-22-222002-22-2-220000000000000000000000000−2i2i−2i2i00000-220000000002i−2i000
χ412-2-22-222-222-2-22-2222-2-2-2002-2-220000000002-2000022-2-2000000002i−2i−2i2i000000000000002i−2i00000
χ422-2-22-222-222-2-22-2222-2-2-2002-2-220000000002-2000022-2-200000000−2i2i2i−2i00000000000000−2i2i00000
χ432-2-22-222-222-2-22-2222-2-2-2002-2-22000000000-220000-2-222000000002i−2i−2i2i00000000000000−2i2i00000
χ442-2-22-222-222-2-22-2222-2-2-2002-2-22000000000-220000-2-22200000000−2i2i2i−2i000000000000002i−2i00000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-24422220000-4000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220000400000022-2-20000000000000000000000000000000000000
χ47444-4-44-4-44000044-4-4-44-400000000000000000000000000000000000004-40000000000000000000
χ48444-4-44-4-44000044-4-4-44-40000000000000000000000000000000000000-440000000000000000000
χ4944-444-4-4-4-244-4-4-222-2-22200-2-222004-4000000000000000000000000000000-220000000000000000
χ5044-444-4-4-4-244-4-4-222-2-22200-2-22200-440000000000000000000000000000002-20000000000000000
χ5144-444-4-4-4-2-4-444-222-2-2220022-2-2000004i−4i000000000000000000000000000000000−2i2i0000000000
χ5244-444-4-4-4-2-4-444-222-2-2220022-2-200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ5344-4-4-4-444400004-44-4-4-444i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ5444-4-4-4-444400004-44-4-4-44−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ5544-4-4-4-444-20000-22-2222-24i−4i000000000000000−2i2i00i6−i6i6−i666−6−600000000000000000000000000000
χ5644-4-4-4-444-20000-22-2222-24i−4i000000000000000−2i2i00−i6i6−i6i6−6−66600000000000000000000000000000
χ5744-4-4-4-444-20000-22-2222-2−4i4i0000000000000002i−2i00i6−i6i6−i6−6−66600000000000000000000000000000
χ5844-4-4-4-444-20000-22-2222-2−4i4i0000000000000002i−2i00−i6i6−i6i666−6−600000000000000000000000000000
χ594-444-4-4-444-44-44-4-4-44-44400-44-440000000000000000000000000000000000000000000000000000
χ604-444-4-4-44-24-44-4222-22-2-200-22-224-40000000000000000000000000000000000-2200000000000000
χ614-444-4-4-44-24-44-4222-22-2-200-22-22-4400000000000000000000000000000000002-200000000000000
χ624-444-4-4-44-2-44-44222-22-2-2002-22-200000000000000000000000000000000000000−2i32i3000000000000
χ634-444-4-4-44-2-44-44222-22-2-2002-22-2000000000000000000000000000000000000002i3−2i3000000000000
χ644-44-44-44-440000-4-44-444-40000000000000−2i22i20000000000−2i22i2−2i22i200000000000000000000000000000
χ654-44-44-44-440000-4-44-444-400000000000002i2−2i200000000002i2−2i22i2−2i200000000000000000000000000000
χ664-44-44-44-4-2000022-22-2-220000000000000−2i22i2000023−23i6−i6−i6i6i2−i2i2−i200000000000000000000000000000
χ674-44-44-44-4-2000022-22-2-220000000000000−2i22i20000−2323−i6i6i6−i6i2−i2i2−i200000000000000000000000000000
χ684-44-44-44-4-2000022-22-2-2200000000000002i2−2i2000023−23−i6i6i6−i6−i2i2−i2i200000000000000000000000000000
χ694-44-44-44-4-2000022-22-2-2200000000000002i2−2i20000−2323i6−i6−i6i6−i2i2−i2i200000000000000000000000000000
χ704-4-44-444-44-444-4-4444-4-4-400-444-40000000000000000000000000000000000000000000000000000
χ714-4-44-444-4-24-4-442-2-2-222200-222-20000000004-40000-2-222000000000000000000000000000000000
χ724-4-44-444-4-24-4-442-2-2-222200-222-2000000000-44000022-2-2000000000000000000000000000000000
χ734-4-44-444-4-2-444-42-2-2-2222002-2-220000000000000000000−2i32i32i3−2i300000000000000000000000000000
χ744-4-44-444-4-2-444-42-2-2-2222002-2-2200000000000000000002i3−2i3−2i32i300000000000000000000000000000
χ754-4-4-444-4440000-44-4-44-44000000000000000000000000000000000000000000000000000000022−220
χ764-4-4-444-4440000-44-4-44-440000000000000000000000000000000000000000000000000000000−22220
χ77888-8-88-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000
χ788-8-8-888-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000

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