Finite Group Databasebeta

← Group #10875947

Character table — Group #10875947

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order122222223444466666664412121212444444488881212121224242424242424244444444444412121212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11
χ41111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1111111-1
χ511111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111111-1-111-1-1-1-1-1
χ611111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111111
χ711111111111111111111111111-1-1-1-11-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ811111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-111-1-111-1-1-1111111-1-1-1
χ1011111111111111111111-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-111-1-111-1-11-1-1-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1111111-111-1-1-1-111-111-1-1-1-111-1
χ1211111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-1-1-1111-1-11111-1-11
χ1311111111111111111111-1-11111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-1-11111-1-1-1-1-111-1-1111
χ1411111111111111111111-1-11111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111111-1-11111-1-1111-1-111-1-1-1
χ1511111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111111-1-111-1-111-1-1-1-1-111-1-11
χ1611111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-11111111-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-2000000002222-2-20000000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-200000000-2-2-2-22200000000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-2220000000022-2-2-2-200000000000002000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-22200000000-2-222220000000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122-2-22-2-2-2-2-2-2-1-1-1-11111111100000000002-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-222222-2-2-2-2-1-1-1-1111111110000000000-21111-1-1-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-12222-2-2-222-2-21111-1-1-1-111110000000000-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-222-2-22211111111-1-1-1-10000000000-2-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-222-2-2-2-2-22211111111-1-1-1-10000000000211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22222-2-21111-1-1-1-111110000000000211-1-111-1-10000000000
χ29222-2-2-2-222-22-22-22-222-2-2002-22-20000000002i−2i000000002i2i−2i−2i00000022-2-200000000002i−2i0000000
χ30222-2-2-2-222-22-22-22-222-2-2002-22-20000000002i−2i000000002i2i−2i−2i000000-2-2220000000000−2i2i0000000
χ31222-2-2-2-222-22-22-22-222-2-2002-22-2000000000−2i2i00000000−2i−2i2i2i00000022-2-20000000000−2i2i0000000
χ32222-2-2-2-222-22-22-22-222-2-2002-22-2000000000−2i2i00000000−2i−2i2i2i000000-2-22200000000002i−2i0000000
χ332-2-22-2-222222-2-2-222-2-2-2200-222-22i−2i0000000000000000000000000002-22-202i−2i00000000000002i−2i0
χ342-2-22-2-222222-2-2-222-2-2-2200-222-22i−2i000000000000000000000000000-22-2202i−2i0000000000000−2i2i0
χ352-2-22-2-222222-2-2-222-2-2-2200-222-2−2i2i0000000000000000000000000002-22-20−2i2i0000000000000−2i2i0
χ362-2-22-2-222222-2-2-222-2-2-2200-222-2−2i2i000000000000000000000000000-22-220−2i2i00000000000002i−2i0
χ372-2-2-222-2222-2-2222-2-2-22-20022-2-2002-200000000000000000002i−2i002i−2i0000000002-2000002i−2i00000
χ382-2-2-222-2222-2-2222-2-2-22-20022-2-2002-20000000000000000000−2i2i00−2i2i0000000002-200000−2i2i00000
χ392-2-2-222-2222-2-2222-2-2-22-20022-2-200-2200000000000000000002i−2i002i−2i000000000-2200000−2i2i00000
χ402-2-2-222-2222-2-2222-2-2-22-20022-2-200-220000000000000000000−2i2i00−2i2i000000000-22000002i−2i00000
χ412-2-2-222-222-222-222-2-2-22-200-2-222000002i−2i00000000000000002i−2i00−2i2i2-2-2200000002i−2i0000000000
χ422-2-2-222-222-222-222-2-2-22-200-2-222000002i−2i0000000000000000−2i2i002i−2i-222-200000002i−2i0000000000
χ432-2-2-222-222-222-222-2-2-22-200-2-22200000−2i2i00000000000000002i−2i00−2i2i-222-20000000−2i2i0000000000
χ442-2-2-222-222-222-222-2-2-22-200-2-22200000−2i2i0000000000000000−2i2i002i−2i2-2-220000000−2i2i0000000000
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
χ47444-4-4-4-4444-44-4-44-444-4-400-44-440000000000000000000000000000000000000000000000000000
χ48444-4-4-4-44-24-44-42-22-2-222002-22-20000000000000002323−23−23000000000000000000000000000000000
χ49444-4-4-4-44-24-44-42-22-2-222002-22-2000000000000000−23−232323000000000000000000000000000000000
χ50444-4-4-4-44-2-44-442-22-2-22200-22-220000000004i−4i00000000−2i−2i2i2i00000000000000000000000000000
χ51444-4-4-4-44-2-44-442-22-2-22200-22-22000000000−4i4i000000002i2i−2i−2i00000000000000000000000000000
χ5244-444-4-4-440000-4-444-44-4000000000000022−2200000022−2222−22000000000000000000000000000000000
χ5344-444-4-4-440000-4-444-44-40000000000000−2222000000−2222−2222000000000000000000000000000000000
χ5444-444-4-4-4-2000022-2-22-22000000000000022−22000023−23−22−226−66−600000000000000000000000000000
χ5544-444-4-4-4-2000022-2-22-22000000000000022−220000−2323−22−22−66−6600000000000000000000000000000
χ5644-444-4-4-4-2000022-2-22-220000000000000−2222000023−232−22−2−66−6600000000000000000000000000000
χ5744-444-4-4-4-2000022-2-22-220000000000000−22220000−23232−22−26−66−600000000000000000000000000000
χ5844-4-4-444-4400004-4-44-4-444i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ5944-4-4-444-4400004-4-44-4-44−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ6044-4-4-444-4-20000-222-222-24i−4i000000000000000−2i2i006−6−66i6−i6−i6i600000000000000000000000000000
χ6144-4-4-444-4-20000-222-222-24i−4i000000000000000−2i2i00−666−6−i6i6i6−i600000000000000000000000000000
χ6244-4-4-444-4-20000-222-222-2−4i4i0000000000000002i−2i006−6−66−i6i6i6−i600000000000000000000000000000
χ6344-4-4-444-4-20000-222-222-2−4i4i0000000000000002i−2i00−666−6i6−i6−i6i600000000000000000000000000000
χ644-444-44-4-4400004-44-44-4-400000000000000000000000000000004-40000000000000000000000000
χ654-444-44-4-4400004-44-44-4-40000000000000000000000000000000-440000000000000000000000000
χ664-44-44-44-440000-4-4-4-444400000000000000000000000000000000000000000000000000000−2i22i2000
χ674-44-44-44-440000-4-4-4-4444000000000000000000000000000000000000000000000000000002i2−2i2000
χ684-4-44-4-4444-4-444-444-4-4-44004-4-440000000000000000000000000000000000000000000000000000
χ694-4-44-4-444-244-4-42-2-2222-2002-2-224i−4i00000000000000000000000000000000−2i2i0000000000000000
χ704-4-44-4-444-244-4-42-2-2222-2002-2-22−4i4i000000000000000000000000000000002i−2i0000000000000000
χ714-4-44-4-444-2-4-4442-2-2222-200-222-200000000000000000000000000000000000023−2300000000000000
χ724-4-44-4-444-2-4-4442-2-2222-200-222-2000000000000000000000000000000000000−232300000000000000
χ734-4-4-444-44-24-4-44-2-2222-2200-2-222004-40000000000000000000000000000000000-22000000000000
χ744-4-4-444-44-24-4-44-2-2222-2200-2-22200-4400000000000000000000000000000000002-2000000000000
χ754-4-4-444-44-2-444-4-2-2222-220022-2-2000004i−4i000000000000000000000000000000000−2i2i0000000000
χ764-4-4-444-44-2-444-4-2-2222-220022-2-200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ778-888-88-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000
χ788-88-88-88-8-400004444-4-4-40000000000000000000000000000000000000000000000000000000000

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