Finite Group Databasebeta

← Group #10845241

Character table — Group #10845241

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order122222223444466666664412121212444444488881212121224242424242424244444444444412121212121212122222488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-11111-1-1-1-111-1-11-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111111
χ511111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1111-1-1-1-11
χ611111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1111111-1-1-11111-1
χ711111111111111111111111111-1-1-1-11-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1
χ811111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11
χ911111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111111-111-1-111-1-1-1-111-111-1-1-1
χ1011111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111-1-111-1-11-1-1111
χ1111111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1
χ1311111111111111111111-1-11111-1-111-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-11111-1-11111-1-1-111-1
χ1411111111111111111111-1-11111-1-111-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11111-1-1-1-1-1-1111-1-11
χ1511111111111111111111-1-11111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-111-1-11111-1-1-111-1-11
χ1611111111111111111111-1-11111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-111-1-111-1-1111-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-20000000022220000-2-20000000000000-200000
χ18222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-200000000-2-2-2-20000220000000000000200000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-2220000000022-2-20000-2-20000000000000200000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-22200000000-2-2220000220000000000000-200000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-2-2-2-2-1-1-1-1111111110000000000-2-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-111111111000000000021111-1-1-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-22222-2-21111-1-1-1-111110000000000-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-2-2-22211111111-1-1-1-100000000002-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-222-222-2-22211111111-1-1-1-10000000000-211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-222-2-2-222-2-21111-1-1-1-111110000000000211-1-111-1-10000000000
χ292222-2-2-2-222-2-222-2-2-222-2002-22-200000002i−2i0000002i2i−2i−2i000000002i2i−2i−2i00000000000002-2000000
χ302222-2-2-2-222-2-222-2-2-222-2002-22-200000002i−2i0000002i2i−2i−2i00000000−2i−2i2i2i0000000000000-22000000
χ312222-2-2-2-222-2-222-2-2-222-2002-22-20000000−2i2i000000−2i−2i2i2i000000002i2i−2i−2i0000000000000-22000000
χ322222-2-2-2-222-2-222-2-2-222-2002-22-20000000−2i2i000000−2i−2i2i2i00000000−2i−2i2i2i00000000000002-2000000
χ332-2-222-2-22222-2-2-22-2-2-2220022-2-22i−2i0000000000000000000002-2002i−2i2i−2i2-202i−2i0000000000000000
χ342-2-222-2-22222-2-2-22-2-2-2220022-2-22i−2i000000000000000000000-2200−2i2i−2i2i-2202i−2i0000000000000000
χ352-2-222-2-22222-2-2-22-2-2-2220022-2-2−2i2i0000000000000000000002-200−2i2i−2i2i2-20−2i2i0000000000000000
χ362-2-222-2-22222-2-2-22-2-2-2220022-2-2−2i2i000000000000000000000-22002i−2i2i−2i-220−2i2i0000000000000000
χ372-2-222-2-222-2-222-22-2-2-22200-2-222002-200000000000000000002-2000000-220002-200002-200000000
χ382-2-222-2-222-2-222-22-2-2-22200-2-222002-20000000000000000000-220000002-20002-20000-2200000000
χ392-2-222-2-222-2-222-22-2-2-22200-2-22200-2200000000000000000002-2000000-22000-220000-2200000000
χ402-2-222-2-222-2-222-22-2-2-22200-2-22200-220000000000000000000-220000002-2000-2200002-200000000
χ412-2-22-222-222-22-2-2-222-22-2002-2-22000002i−2i000000000000000000002-2-2200000002i−2i00000002i−2i000
χ422-2-22-222-222-22-2-2-222-22-2002-2-22000002i−2i00000000000000000000-222-200000002i−2i0000000−2i2i000
χ432-2-22-222-222-22-2-2-222-22-2002-2-2200000−2i2i000000000000000000002-2-220000000−2i2i0000000−2i2i000
χ442-2-22-222-222-22-2-2-222-22-2002-2-2200000−2i2i00000000000000000000-222-20000000−2i2i00000002i−2i000
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
χ474444-4-4-4-44-444-44-4-4-444-400-44-440000000000000000000000000000000000000000000000000000
χ484444-4-4-4-4-24-4-44-2222-2-2200-22-2200000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ494444-4-4-4-4-24-4-44-2222-2-2200-22-220000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ504444-4-4-4-4-2-444-4-2222-2-22002-22-200000000000000000002323−23−2300000000000000000000000000000
χ514444-4-4-4-4-2-444-4-2222-2-22002-22-20000000000000000000−23−23232300000000000000000000000000000
χ5244-4-444-4-440000444-4-4-4-400000000000000022−220000000022−2222−2200000000000000000000000000000
χ5344-4-444-4-440000444-4-4-4-4000000000000000−222200000000−2222−222200000000000000000000000000000
χ5444-4-444-4-4-20000-2-2-2222200000000000000022−2200−2i32i3i6−i6i6−i6−22−2200000000000000000000000000000
χ5544-4-444-4-4-20000-2-2-2222200000000000000022−22002i3−2i3−i6i6−i6i6−22−2200000000000000000000000000000
χ5644-4-444-4-4-20000-2-2-22222000000000000000−222200−2i32i3−i6i6−i6i62−22−200000000000000000000000000000
χ5744-4-444-4-4-20000-2-2-22222000000000000000−2222002i3−2i3i6−i6i6−i62−22−200000000000000000000000000000
χ5844-4-4-4-444400004-4-44-4-444-40000000000000004-4000000000000000000000000000000000000000
χ5944-4-4-4-444400004-4-44-4-44-44000000000000000-44000000000000000000000000000000000000000
χ6044-4-4-4-444-20000-222-222-24-4000000000000000-22006−6−666−6−6600000000000000000000000000000
χ6144-4-4-4-444-20000-222-222-24-4000000000000000-2200−666−6−666−600000000000000000000000000000
χ6244-4-4-4-444-20000-222-222-2-440000000000000002-2006−6−66−666−600000000000000000000000000000
χ6344-4-4-4-444-20000-222-222-2-440000000000000002-200−666−66−6−6600000000000000000000000000000
χ644-44-44-44-440000-44-444-4-40000000000000000000000000000000000000000000000000000000−2i22i20
χ654-44-44-44-440000-44-444-4-400000000000000000000000000000000000000000000000000000002i2−2i20
χ664-44-4-44-4440000-4-44-44-4400000000000000000000000000000004-40000000000000000000000000
χ674-44-4-44-4440000-4-44-44-440000000000000000000000000000000-440000000000000000000000000
χ684-4-444-4-44-244-4-42-2222-2-200-2-2224i−4i00000000000000000000000000000000−2i2i0000000000000000
χ694-4-444-4-44-244-4-42-2222-2-200-2-222−4i4i000000000000000000000000000000002i−2i0000000000000000
χ704-4-444-4-44-2-4-4442-2222-2-20022-2-2004-400000000000000000000000000000000-2200000000000000
χ714-4-444-4-44-2-4-4442-2222-2-20022-2-200-44000000000000000000000000000000002-200000000000000
χ724-4-44-444-44-44-44-4-444-44-400-444-40000000000000000000000000000000000000000000000000000
χ734-4-44-444-4-24-44-422-2-22-2200-222-2000004i−4i0000000000000000000000000000000−2i2i000000000000
χ744-4-44-444-4-24-44-422-2-22-2200-222-200000−4i4i00000000000000000000000000000002i−2i000000000000
χ754-4-44-444-4-2-44-4422-2-22-22002-2-22000000000000000000000000000000000000000023−230000000000
χ764-4-44-444-4-2-44-4422-2-22-22002-2-220000000000000000000000000000000000000000−23230000000000
χ778-88-88-88-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000
χ788-88-8-88-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000

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