Finite Group Databasebeta

← Group #10840263

Character table — Group #10840263

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666622121212124444444668888121224242424242424244444444444412121212121212122444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-111-1-111-1-11-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-111111
χ511111111111111111111111111-1-111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111111-1-1-1-1-1-11
χ611111111111111111111111111-1-111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1111111-1
χ711111111111111111111111111-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ811111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-111111111-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1
χ1011111111111111111111-1-111111111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-11111-1-1-1-11-1-1-1-111-1-11
χ1111111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-111-1-1-11111-1-11
χ1211111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-111111-1-1-1-111-1
χ1311111111111111111111-1-11111-1-11111-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11111-1-1-111-1-111-1-1-1
χ1411111111111111111111-1-11111-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11111-1-11-1-111-1-1111
χ1511111111111111111111-1-11111-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-11111-1-111111-1-1-1-11111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-11111-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111111-1-1-1
χ17222222222-2-2-2-2222222222-2-2-2-2000000-2220000-2-20000000022-2-2-2-200000000000002000000000
χ18222222222-2-2-2-2222222222-2-2-2-2000000-2220000-2-200000000-2-222220000000000000-2000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-20000002-2-20000220000000022-2-2220000000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-20000002-2-200002200000000-2-222-2-200000000000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122-2-2222-1-1-2-2-2-2-1-1111111110000000000-2-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-222-2-22-1-1-2-2-2-2-1-1111111110000000000211-1-111-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-22-1-12222-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-12222-2-2-211-2-22211-1-1-1-111110000000000-2-1-1-1-111110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-21122-2-2111111-1-1-1-100000000002-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-22222-21122-2-2111111-1-1-1-10000000000-211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-222-211-2-22211-1-1-1-11111000000000021111-1-1-1-10000000000
χ2922-2-2-222-222-22-22-2-22-2-220022-2-20000000002i−2i000000002i2i−2i−2i0000002i2i−2i−2i00000000002-20000000
χ3022-2-2-222-222-22-22-2-22-2-220022-2-20000000002i−2i000000002i2i−2i−2i000000−2i−2i2i2i0000000000-220000000
χ3122-2-2-222-222-22-22-2-22-2-220022-2-2000000000−2i2i00000000−2i−2i2i2i0000002i2i−2i−2i0000000000-220000000
χ3222-2-2-222-222-22-22-2-22-2-220022-2-2000000000−2i2i00000000−2i−2i2i2i000000−2i−2i2i2i00000000002-20000000
χ332-22-2-2-222222-2-2-22-222-2-2002-22-2002i−2i00000000000000000000000002-22-20002i−2i0000000002i−2i000
χ342-22-2-2-222222-2-2-22-222-2-2002-22-2002i−2i0000000000000000000000000-22-220002i−2i000000000−2i2i000
χ352-22-2-2-222222-2-2-22-222-2-2002-22-200−2i2i00000000000000000000000002-22-2000−2i2i000000000−2i2i000
χ362-22-2-2-222222-2-2-22-222-2-2002-22-200−2i2i0000000000000000000000000-22-22000−2i2i0000000002i−2i000
χ372-2-222-22-222-2-22-2-222-22-2002-2-2200002i−2i000000000000000002-22-2002i−2i−2i2i000002i−2i000000000000
χ382-2-222-22-222-2-22-2-222-22-2002-2-2200002i−2i00000000000000000-22-2200−2i2i2i−2i000002i−2i000000000000
χ392-2-222-22-222-2-22-2-222-22-2002-2-220000−2i2i000000000000000002-22-200−2i2i2i−2i00000−2i2i000000000000
χ402-2-222-22-222-2-22-2-222-22-2002-2-220000−2i2i00000000000000000-22-22002i−2i−2i2i00000−2i2i000000000000
χ412-2-222-22-22-222-2-2-222-22-200-222-22i−2i0000000000000000000002-2-2200000002i−2i0000000002i−2i00000
χ422-2-222-22-22-222-2-2-222-22-200-222-22i−2i000000000000000000000-222-200000002i−2i000000000−2i2i00000
χ432-2-222-22-22-222-2-2-222-22-200-222-2−2i2i0000000000000000000002-2-220000000−2i2i000000000−2i2i00000
χ442-2-222-22-22-222-2-2-222-22-200-222-2−2i2i000000000000000000000-222-20000000−2i2i0000000002i−2i00000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-2442222000000-4-2-20000220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220000004220000-2-20000000000000000000000000000000000000
χ47444-44-4-4-4400004-4-4-444-40000000000000000022−22002222−22−22000000000000000000000000000000000
χ48444-44-4-4-4400004-4-4-444-400000000000000000−222200−22−222222000000000000000000000000000000000
χ49444-44-4-4-4-20000-2222-2-220000000000000000022−2223−23−2−2226−66−600000000000000000000000000000
χ50444-44-4-4-4-20000-2222-2-220000000000000000022−22−2323−2−222−66−6600000000000000000000000000000
χ51444-44-4-4-4-20000-2222-2-2200000000000000000−222223−2322−2−2−66−6600000000000000000000000000000
χ52444-44-4-4-4-20000-2222-2-2200000000000000000−2222−232322−2−26−66−600000000000000000000000000000
χ5344-44-4-4-4440000444-4-4-4-44-4000000000004-40000000000000000000000000000000000000000000
χ5444-44-4-4-4440000444-4-4-4-4-4400000000000-440000000000000000000000000000000000000000000
χ5544-44-4-4-44-20000-2-2-222224-400000000000-22000000i6−i6i6−i6i6−i6−i6i600000000000000000000000000000
χ5644-44-4-4-44-20000-2-2-222224-400000000000-22000000−i6i6−i6i6−i6i6i6−i600000000000000000000000000000
χ5744-44-4-4-44-20000-2-2-22222-44000000000002-2000000i6−i6i6−i6−i6i6i6−i600000000000000000000000000000
χ5844-44-4-4-44-20000-2-2-22222-44000000000002-2000000−i6i6−i6i6i6−i6−i6i600000000000000000000000000000
χ5944-4-4-444-44-44-444-4-44-4-4400-4-4440000000000000000000000000000000000000000000000000000
χ6044-4-4-444-4-24-44-4-222-222-200-2-2220000000004i−4i00000000−2i−2i2i2i00000000000000000000000000000
χ6144-4-4-444-4-24-44-4-222-222-200-2-222000000000−4i4i000000002i2i−2i−2i00000000000000000000000000000
χ6244-4-4-444-4-2-44-44-222-222-20022-2-2000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ6344-4-4-444-4-2-44-44-222-222-20022-2-20000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ644-444-44-4-440000-4-44-44-440000000000000000000000000000000004i−4i00000000000000000000000
χ654-444-44-4-440000-4-44-44-44000000000000000000000000000000000−4i4i00000000000000000000000
χ664-44-4-4-4444-4-444-44-444-4-400-44-440000000000000000000000000000000000000000000000000000
χ674-44-4-4-444-244-4-42-22-2-22200-22-22004i−4i00000000000000000000000000000000−2i2i00000000000000
χ684-44-4-4-444-244-4-42-22-2-22200-22-2200−4i4i000000000000000000000000000000002i−2i00000000000000
χ694-44-4-4-444-2-4-4442-22-2-222002-22-2000000000000000000000000000000000000000023−230000000000
χ704-44-4-4-444-2-4-4442-22-2-222002-22-20000000000000000000000000000000000000000−23230000000000
χ714-4-444-44-4-24-4-4422-2-22-2200-222-200004i−4i00000000000000000000000000000000−2i2i000000000000
χ724-4-444-44-4-24-4-4422-2-22-2200-222-20000−4i4i000000000000000000000000000000002i−2i000000000000
χ734-4-444-44-4-2-444-422-2-22-22002-2-224i−4i00000000000000000000000000000000−2i2i0000000000000000
χ744-4-444-44-4-2-444-422-2-22-22002-2-22−4i4i000000000000000000000000000000002i−2i0000000000000000
χ754-4-4-444-4440000-44-4-4-444000000000000000000000000000000000000000000000000000000022−220
χ764-4-4-444-4440000-44-4-4-4440000000000000000000000000000000000000000000000000000000−22220
χ778-888-88-8-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-888-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000

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