Finite Group Databasebeta

← Group #10846320

Character table — Group #10846320

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444446666888888888888888888881212121212121616161616161616161624242424242424244848
order122222223444466666668888121212124444244444668812122424242424242424448888226666121212122244448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1
χ311111111111111111111111111111111-11111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-111-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111
χ71111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ911111111111111111111-1-1-1-111111111111-1-1111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111-1-1111-1-11-1-11-1
χ1011111111111111111111-1-1-1-1111111111-1-111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111-1-11111-1-1-11
χ1111111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-111-1-1-1-111-11
χ1211111111111111111111-1-1-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-1-111-1111-1
χ1311111111111111111111-1-1-1-11111-1-1-1-1111-1-1111-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-1-111-111-11
χ1411111111111111111111-1-1-1-11111-1-1-1-11-1-111111-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-11111-1-1-1-1111-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-11111-11-1-11111-1-1-1-11111-1-11-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-111111-111-1-1-1-111111-1-11-1-1-11
χ17222222222-2-2-2-222222220000-2-2-2-2222220000-22200-2-200000000-2-20000000000000000-20020000
χ18222222222-2-2-2-222222220000-2-2-2-22222-200002-2-2002200000000-2-20000000000000000200-20000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-220000-22200-2-200000000220000000000000000200-20000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-200002-2-2002200000000220000000000000000-20020000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-10000222222-1-122-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-100002-2-2-2-22-1-122-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-22222-211-2-211-1-1-1-11111000000-2-21111-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-2-211-2-211-1-1-1-1111100000022-1-1-1-111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000222-2-22-1-1-2-2-1-1111111110000002-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100002-2-2222-1-1-2-2-1-111111111000000-2211-1-111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-222-2-2-21122111111-1-1-1-1000000-2211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-2-222-21122111111-1-1-1-10000002-2-1-11111-1-10000000000
χ29222-2-2-22-2222-2-222-2-22-2-222-2-22-2-222i2i−2i−2i00000000000022-2-200002i−2i2i2i−2i−2i00000000000000000000
χ30222-2-2-22-2222-2-222-2-22-2-222-2-22-2-22−2i−2i2i2i00000000000022-2-20000−2i2i−2i−2i2i2i00000000000000000000
χ31222-2-2-22-2222-2-222-2-22-2-2-2-2222-2-222i2i−2i−2i000000000000-2-22200002i−2i−2i−2i2i2i00000000000000000000
χ32222-2-2-22-2222-2-222-2-22-2-2-2-2222-2-22−2i−2i2i2i000000000000-2-2220000−2i2i2i2i−2i−2i00000000000000000000
χ33222-2-2-22-22-2-22222-2-22-2-20000-222-22i2i−2i−2i000000002i−2i0000002i2i−2i−2i−2i2i000000000000000000002-200
χ34222-2-2-22-22-2-22222-2-22-2-20000-222-22i2i−2i−2i00000000−2i2i000000−2i−2i2i2i−2i2i00000000000000000000-2200
χ35222-2-2-22-22-2-22222-2-22-2-20000-222-2−2i−2i2i2i000000002i−2i0000002i2i−2i−2i2i−2i00000000000000000000-2200
χ36222-2-2-22-22-2-22222-2-22-2-20000-222-2−2i−2i2i2i00000000−2i2i000000−2i−2i2i2i2i−2i000000000000000000002-200
χ372-2-22-2-2222-222-2-2-2222-2-22-22-2-22-2200000000000000002-22-2000000000000000000002-202-200000
χ382-2-22-2-2222-222-2-2-2222-2-22-22-2-22-2200000000000000002-22-200000000000000000000-220-2200000
χ392-2-22-2-2222-222-2-2-2222-2-2-22-22-22-220000000000000000-22-22000000000000000000002-20-2200000
χ402-2-22-2-2222-222-2-2-2222-2-2-22-22-22-220000000000000000-22-2200000000000000000000-2202-200000
χ412-2-2-2222-22-22-22-2-2-2-22222-2-22-2-222000002-22-200000002-2-2200000000000000002-22-20000000000
χ422-2-2-2222-22-22-22-2-2-2-22222-2-22-2-22200000-22-2200000002-2-220000000000000000-22-220000000000
χ432-2-2-2222-22-22-22-2-2-2-2222-222-2-2-222000002-2-220000000-222-200000000000000002-2-220000000000
χ442-2-2-2222-22-22-22-2-2-2-2222-222-2-2-22200000-222-20000000-222-20000000000000000-222-20000000000
χ452-2-2-2222-2-1-22-221111-1-1-12-2-2211-1-1000002-22-20−i3i300−i3i3-111-1−i3i3−i3i300000000−i3i3−i3i3-11-110000000000
χ462-2-2-2222-2-1-22-221111-1-1-12-2-2211-1-1000002-22-20i3−i300i3−i3-111-1i3−i3i3−i300000000i3−i3i3−i3-11-110000000000
χ472-2-2-2222-2-1-22-221111-1-1-12-2-2211-1-100000-22-220−i3i300−i3i3-111-1−i3i3−i3i300000000i3−i3i3−i31-11-10000000000
χ482-2-2-2222-2-1-22-221111-1-1-12-2-2211-1-100000-22-220i3−i300i3−i3-111-1i3−i3i3−i300000000−i3i3−i3i31-11-10000000000
χ492-2-2-2222-2-1-22-221111-1-1-1-222-211-1-1000002-2-220−i3i300−i3i31-1-11i3−i3i3−i300000000−i3i3i3−i3-111-10000000000
χ502-2-2-2222-2-1-22-221111-1-1-1-222-211-1-1000002-2-220i3−i300i3−i31-1-11−i3i3−i3i300000000i3−i3−i3i3-111-10000000000
χ512-2-2-2222-2-1-22-221111-1-1-1-222-211-1-100000-222-20−i3i300−i3i31-1-11i3−i3i3−i300000000i3−i3−i3i31-1-110000000000
χ522-2-2-2222-2-1-22-221111-1-1-1-222-211-1-100000-222-20i3−i300i3−i31-1-11−i3i3−i3i300000000−i3i3i3−i31-1-110000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200002222000040000-4-2-200220000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000-4000042200-2-20000000000000000000000000000000000
χ55444-4-4-44-4-244-4-4-2-222-22244-4-4-222-20000000000000000-2-222000000000000000000000000000000
χ56444-4-4-44-4-244-4-4-2-222-222-4-444-222-2000000000000000022-2-2000000000000000000000000000000
χ57444-4-4-44-4-2-4-444-2-222-22200002-2-220000000000004i−4i000000−2i−2i2i2i00000000000000000000000000
χ58444-4-4-44-4-2-4-444-2-222-22200002-2-22000000000000−4i4i0000002i2i−2i−2i00000000000000000000000000
χ5944-444-4-4-4400004-44-4-44-40000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6044-444-4-4-4400004-44-4-44-400000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ6144-4-4-44-44400004-4-44-4-44000000000000000000000000000000000022−22−222200000000000000000000
χ6244-4-4-44-44400004-4-44-4-440000000000000000000000000000000000−222222−2200000000000000000000
χ634-444-44-4-440000-444-4-4-44000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ644-444-44-4-440000-444-4-4-4400000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ654-44-44-4-4440000-44-44-44-4000000004-4-440000000000000000000000000000000000000000000000
χ664-44-44-4-4440000-44-44-44-400000000-444-40000000000000000000000000000000000000000000000
χ674-4-44-4-44444-4-44-4-4444-4-400004-44-400000000000000000000000000000000000000000000000000
χ684-4-44-4-444-24-4-4422-2-2-2220000-22-220000000000000000000023−23−232300000000000000000000000000
χ694-4-44-4-444-24-4-4422-2-2-2220000-22-2200000000000000000000−232323−2300000000000000000000000000
χ704-4-44-4-444-2-444-422-2-2-2224-44-42-22-20000000000000000-22-22000000000000000000000000000000
χ714-4-44-4-444-2-444-422-2-2-222-44-442-22-200000000000000002-22-2000000000000000000000000000000
χ724-4-4-4444-444-44-4-4-4-4-4444000044-4-400000000000000000000000000000000000000000000000000
χ734-4-4-4444-4-24-44-42222-2-2-20000-2-2220000000000−2i32i3002i3−2i30000000000000000000000000000000000
χ744-4-4-4444-4-24-44-42222-2-2-20000-2-22200000000002i3−2i300−2i32i30000000000000000000000000000000000
χ7588-888-8-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000
χ7688-8-8-88-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000
χ778-888-88-8-8-400004-4-4444-40000000000000000000000000000000000000000000000000000000000
χ788-88-88-8-88-400004-44-44-440000000000000000000000000000000000000000000000000000000000

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