Finite Group Databasebeta

← Group #10831732

Character table — Group #10831732

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212122244444888812121212242424242424242444444444444661212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-1111111-1
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
χ711111111111111111111111111-1-11-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ811111111111111111111111111-1-11-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111111-111-1-111-1-1-111-1-111-1-1-1
χ1011111111111111111111-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11-1-111-1-1111
χ1111111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-111-1-1-1-111-11111-1-111-1
χ1211111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-1-1-1111-1-1-1-111-1-11
χ1311111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111111-1-11111-1-1-1-1-1-1-1-1-1111
χ1411111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-11111-1-11111111-1-1-1
χ1511111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-111-1-111-1-1-11111-1-11
χ1611111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-111-1-111111-1-1-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-20000000022220000-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-200000000-2-2-2-20000220000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-2220000000022-2-20000-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-22200000000-2-222000022000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-11111111100000000002-1-1-1-111110000000000
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
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-222-2-222-2-21111-1-1-1-111110000000000-2-1-111-1-1110000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-2-2-22211111111-1-1-1-10000000000211-1-1-1-1110000000000
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
χ29222-2-22-2-222-22-222-22-2-2-20022-2-22-2000000000000000000000000022-2-20002-2000000000002-2000
χ30222-2-22-2-222-22-222-22-2-2-20022-2-22-20000000000000000000000000-2-2220002-200000000000-22000
χ31222-2-22-2-222-22-222-22-2-2-20022-2-2-22000000000000000000000000022-2-2000-2200000000000-22000
χ32222-2-22-2-222-22-222-22-2-2-20022-2-2-220000000000000000000000000-2-222000-22000000000002-2000
χ332-2-2222-2-22-2-222-2-222-22-2002-22-200000002i−2i0000002i2i−2i−2i000000002-22-20000000000002i−2i0000000
χ342-2-2222-2-22-2-222-2-222-22-2002-22-200000002i−2i0000002i2i−2i−2i00000000-22-22000000000000−2i2i0000000
χ352-2-2222-2-22-2-222-2-222-22-2002-22-20000000−2i2i000000−2i−2i2i2i000000002-22-2000000000000−2i2i0000000
χ362-2-2222-2-22-2-222-2-222-22-2002-22-20000000−2i2i000000−2i−2i2i2i00000000-22-220000000000002i−2i0000000
χ372-2-2-2-222222-2-22-2-2-222-2200-222-2000002-200000000000000002-20000002-200000002-20002-200000
χ382-2-2-2-222222-2-22-2-2-222-2200-222-2000002-20000000000000000-22000000-2200000002-2000-2200000
χ392-2-2-2-222222-2-22-2-2-222-2200-222-200000-2200000000000000002-20000002-20000000-22000-2200000
χ402-2-2-2-222222-2-22-2-2-222-2200-222-200000-220000000000000000-22000000-220000000-220002-200000
χ412-2-2-2-22222-222-2-2-2-222-22002-2-220002-20000000000000000002-2002-2-22-22000002-2000000000000
χ422-2-2-2-22222-222-2-2-2-222-22002-2-220002-2000000000000000000-2200-222-22-2000002-2000000000000
χ432-2-2-2-22222-222-2-2-2-222-22002-2-22000-220000000000000000002-200-222-2-2200000-22000000000000
χ442-2-2-2-22222-222-2-2-2-222-22002-2-22000-22000000000000000000-22002-2-222-200000-22000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244222200-400000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220040000000022-2-20000000000000000000000000000000000000
χ47444-4-44-4-44-44-4444-44-4-4-400-4-4440000000000000000000000000000000000000000000000000000
χ48444-4-44-4-4-24-44-4-2-22-222200-2-2224-400000000000000000000000000000000-220000000000000000
χ49444-4-44-4-4-24-44-4-2-22-222200-2-222-44000000000000000000000000000000002-20000000000000000
χ50444-4-44-4-4-2-44-44-2-22-22220022-2-200000000000000000000000000000000000023−2300000000000000
χ51444-4-44-4-4-2-44-44-2-22-22220022-2-2000000000000000000000000000000000000−232300000000000000
χ5244-44-4-44-4400004-4-4-444-44-40000000000000004-4000000000000000000000000000000000000000
χ5344-44-4-44-4400004-4-4-444-4-44000000000000000-44000000000000000000000000000000000000000
χ5444-44-4-44-4-20000-2222-2-224-4000000000000000-22006−66−666−6−600000000000000000000000000000
χ5544-44-4-44-4-20000-2222-2-224-4000000000000000-2200−66−66−6−66600000000000000000000000000000
χ5644-44-4-44-4-20000-2222-2-22-440000000000000002-2006−66−6−6−66600000000000000000000000000000
χ5744-44-4-44-4-20000-2222-2-22-440000000000000002-200−66−6666−6−600000000000000000000000000000
χ5844-4-44-4-44400004-44-4-4-44000000000000000000000000000000000000000000000000000000022−220
χ5944-4-44-4-44400004-44-4-4-440000000000000000000000000000000000000000000000000000000−22220
χ604-444-4-4-4440000-44-4-4-44400000000000000022−220000000022−2222−2200000000000000000000000000000
χ614-444-4-4-4440000-44-4-4-444000000000000000−222200000000−2222−222200000000000000000000000000000
χ624-444-4-4-44-200002-2222-2-200000000000000022−2200−2i32i3i6−i6−i6i6−22−2200000000000000000000000000000
χ634-444-4-4-44-200002-2222-2-200000000000000022−22002i3−2i3−i6i6i6−i6−22−2200000000000000000000000000000
χ644-444-4-4-44-200002-2222-2-2000000000000000−222200−2i32i3−i6i6i6−i62−22−200000000000000000000000000000
χ654-444-4-4-44-200002-2222-2-2000000000000000−2222002i3−2i3i6−i6−i6i62−22−200000000000000000000000000000
χ664-44-44-44-440000-444-44-4-400000000000000000000000000000004-40000000000000000000000000
χ674-44-44-44-440000-444-44-4-40000000000000000000000000000000-440000000000000000000000000
χ684-4-4444-4-4444-4-4-4-444-44-400-44-440000000000000000000000000000000000000000000000000000
χ694-4-4444-4-4-244-4-422-2-22-22002-22-2000000000000000000023−23−232300000000000000000000000000000
χ704-4-4444-4-4-244-4-422-2-22-22002-22-20000000000000000000−232323−2300000000000000000000000000000
χ714-4-4444-4-4-2-4-44422-2-22-2200-22-2200000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ724-4-4444-4-4-2-4-44422-2-22-2200-22-220000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ734-4-4-4-4444-24-4-44222-2-22-2002-2-22000004-4000000000000000000000000000000000-220000000000
χ744-4-4-4-4444-24-4-44222-2-22-2002-2-2200000-440000000000000000000000000000000002-20000000000
χ754-4-4-4-4444-2-444-4222-2-22-200-222-20004-4000000000000000000000000000000000-22000000000000
χ764-4-4-4-4444-2-444-4222-2-22-200-222-2000-440000000000000000000000000000000002-2000000000000
χ7788-8-88-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000
χ788-88-88-88-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000

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