Finite Group Databasebeta

← Group #10827618

Character table — Group #10827618

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666622121212124444444668888121224242424242424242244444444412121212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-111-1-111-1-1111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11111111
χ511111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1111-1-111-1-1-1-11
χ611111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-111-1-11111-1
χ711111111111111111111111111-1-11-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ811111111111111111111111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111111-111-1-1-1-111-1-1-111-1-111-1
χ1011111111111111111111-1-1111111-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-11
χ1111111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-111-1-11
χ1211111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-1-1-111111-1-111-1
χ1311111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11111-1111111-1-1-1
χ1411111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1-1111
χ1511111111111111111111-1-11111-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-11-1-11111-1-1-111-1-1-1-1111
χ1611111111111111111111-1-11111-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111111-1-11111-1-11-1-11111-1-1-1
χ17222222222-2-2-2-2222222222-2-2-2-200-20000220000-2-20000000022-2-2-2-200000000000002000000000
χ18222222222-2-2-2-2222222222-2-2-2-200-20000220000-2-200000000-2-222220000000000000-2000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-20020000-2-2000022000000002222-2-20000000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-20020000-2-200002200000000-2-2-2-22200000000000002000000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-100000000002-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-1-1-2-2-2-2-1-1111111110000000000-2-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-222-1-1-2-2-2-2-1-1111111110000000000211-1-111-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-22211-2-22211-1-1-1-111110000000000-2-1-11111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-21122-2-2111111-1-1-1-100000000002-1-1-1-111110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222221122-2-2111111-1-1-1-10000000000-21111-1-1-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-211-2-22211-1-1-1-111110000000000211-1-1-1-1110000000000
χ2922-22-2-22-2222-2-22-2-2-22-22002-22-2000002-200000000000000000000002i2i−2i−2i00000002-200000002i−2i0
χ3022-22-2-22-2222-2-22-2-2-22-22002-22-2000002-20000000000000000000000−2i−2i2i2i00000002-20000000−2i2i0
χ3122-22-2-22-2222-2-22-2-2-22-22002-22-200000-2200000000000000000000002i2i−2i−2i0000000-220000000−2i2i0
χ3222-22-2-22-2222-2-22-2-2-22-22002-22-200000-220000000000000000000000−2i−2i2i2i0000000-2200000002i−2i0
χ332-22-2-222-222-22-2-222-2-2-220022-2-2000000000002i−2i002i2i−2i−2i00000000002i−2i2i−2i0000000000002-200000
χ342-22-2-222-222-22-2-222-2-2-220022-2-2000000000002i−2i002i2i−2i−2i0000000000−2i2i−2i2i000000000000-2200000
χ352-22-2-222-222-22-2-222-2-2-220022-2-200000000000−2i2i00−2i−2i2i2i00000000002i−2i2i−2i000000000000-2200000
χ362-22-2-222-222-22-2-222-2-2-220022-2-200000000000−2i2i00−2i−2i2i2i0000000000−2i2i−2i2i0000000000002-200000
χ372-2-2-22-22222-2-22-2-2-22-222002-2-222-20000000000000000000002-2002-22-2-2202-20000000000000000
χ382-2-2-22-22222-2-22-2-2-22-222002-2-222-2000000000000000000000-2200-22-222-202-20000000000000000
χ392-2-2-22-22222-2-22-2-2-22-222002-2-22-220000000000000000000002-2002-2-222-20-220000000000000000
χ402-2-2-22-22222-2-22-2-2-22-222002-2-22-22000000000000000000000-2200-222-2-220-220000000000000000
χ412-2-2-22-2222-222-2-2-2-22-22200-222-20002-20000000000000000002-200-220000000002-20002-20000000
χ422-2-2-22-2222-222-2-2-2-22-22200-222-20002-2000000000000000000-22002-20000000002-2000-220000000
χ432-2-2-22-2222-222-2-2-2-22-22200-222-2000-220000000000000000002-200-22000000000-22000-220000000
χ442-2-2-22-2222-222-2-2-2-22-22200-222-2000-22000000000000000000-22002-2000000000-220002-20000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244222200-40000-2-20000220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220040000220000-2-20000000000000000000000000000000000000
χ47444-4-4-4-444000044-44-4-4-44-4000000000004-40000000000000000000000000000000000000000000
χ48444-4-4-4-444000044-44-4-4-4-4400000000000-440000000000000000000000000000000000000000000
χ49444-4-4-4-44-20000-2-22-22224-400000000000-22000000i6−i6i6−i6i6i6−i6−i600000000000000000000000000000
χ50444-4-4-4-44-20000-2-22-22224-400000000000-22000000−i6i6−i6i6−i6−i6i6i600000000000000000000000000000
χ51444-4-4-4-44-20000-2-22-2222-44000000000002-2000000i6−i6i6−i6−i6−i6i6i600000000000000000000000000000
χ52444-4-4-4-44-20000-2-22-2222-44000000000002-2000000−i6i6−i6i6i6i6−i6−i600000000000000000000000000000
χ5344-44-4-44-44-4-4444-4-4-44-4400-44-440000000000000000000000000000000000000000000000000000
χ5444-44-4-44-4-244-4-4-2222-22-200-22-22000004-4000000000000000000000000000000000-220000000000
χ5544-44-4-44-4-244-4-4-2222-22-200-22-2200000-440000000000000000000000000000000002-20000000000
χ5644-44-4-44-4-2-4-444-2222-22-2002-22-2000000000000000000000000000000000000−2i32i300000000000000
χ5744-44-4-44-4-2-4-444-2222-22-2002-22-20000000000000000000000000000000000002i3−2i300000000000000
χ5844-4-444-4-4400004-44-4-44-40000000000000000000000000000000000000000000000000000022−22000
χ5944-4-444-4-4400004-44-4-44-400000000000000000000000000000000000000000000000000000−2222000
χ604-4444-4-4-440000-44-4-444-400000000000000022−220000000022−2222−2200000000000000000000000000000
χ614-4444-4-4-440000-44-4-444-4000000000000000−222200000000−2222−222200000000000000000000000000000
χ624-4444-4-4-4-200002-222-2-2200000000000000022−220023−236−6−66−22−2200000000000000000000000000000
χ634-4444-4-4-4-200002-222-2-2200000000000000022−2200−2323−666−6−22−2200000000000000000000000000000
χ644-4444-4-4-4-200002-222-2-22000000000000000−22220023−23−666−62−22−200000000000000000000000000000
χ654-4444-4-4-4-200002-222-2-22000000000000000−222200−23236−6−662−22−200000000000000000000000000000
χ664-44-4-444-44-44-44-444-4-4-4400-4-4440000000000000000000000000000000000000000000000000000
χ674-44-4-444-4-24-44-42-2-2222-200-2-222000000000004i−4i00−2i−2i2i2i000000000000000000000000000000000
χ684-44-4-444-4-24-44-42-2-2222-200-2-22200000000000−4i4i002i2i−2i−2i000000000000000000000000000000000
χ694-44-4-444-4-2-44-442-2-2222-20022-2-20000000000000000000−2i32i32i3−2i300000000000000000000000000000
χ704-44-4-444-4-2-44-442-2-2222-20022-2-200000000000000000002i3−2i3−2i32i300000000000000000000000000000
χ714-4-44-44-4440000-4-4444-4-400000000000000000000000000000004i−4i0000000000000000000000000
χ724-4-44-44-4440000-4-4444-4-40000000000000000000000000000000−4i4i0000000000000000000000000
χ734-4-4-44-444-24-4-44222-22-2-200-222-24-400000000000000000000000000000000-220000000000000000
χ744-4-4-44-444-24-4-44222-22-2-200-222-2-44000000000000000000000000000000002-20000000000000000
χ754-4-4-44-444-2-444-4222-22-2-2002-2-220004-4000000000000000000000000000000000-22000000000000
χ764-4-4-44-444-2-444-4222-22-2-2002-2-22000-440000000000000000000000000000000002-2000000000000
χ7788-8-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000
χ788-8-88-88-88-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000

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