Finite Group Databasebeta

← Group #10848868

Character table — Group #10848868

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444466666664444888812121212121212122244666688121212121212242424242424242444448888246612122444448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ911111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-1-111-1-111-1-1-1-1-11
χ1011111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111111-1
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-111-1-1-1-1-1-111-1-11-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-111-11
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-11111-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-11-1-1111111-1-1-1-11-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200000000002200000000000022-2-20000000000-2200000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2000000000022000000000000-2-22200000000002-200000000
χ19222222222-2-2-2-22222222-2-2220000-2-22222-2-20000000000-2-200000000000022-2-200000000002-200000000
χ20222222222-2-2-2-22222222-2-2220000-2-22222-2-20000000000-2-2000000000000-2-2220000000000-2200000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-1-11111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-122-2-2-1-1-1-1-2-2111111-1-1-1-1111100000000-2211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-2221111-2-211-1-1-1-1-1-1-1-11111000000002-2-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-2-2-1-1-1-1221111111111-1-1-1-1000000002-2-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-2-22211112211-1-1-1-11111-1-1-1-100000000-2211-1-10000000000
χ29222-2-2-22-222-22-222-22-2-2-22i−2i2i−2i00002-22i2i−2i−2i2-200000000002i−2i00000000000000002i2i−2i−2i0000000000002-200
χ30222-2-2-22-222-22-222-22-2-2-22i−2i2i−2i00002-22i2i−2i−2i2-200000000002i−2i0000000000000000−2i−2i2i2i000000000000-2200
χ31222-2-2-22-222-22-222-22-2-2-2−2i2i−2i2i00002-2−2i−2i2i2i2-20000000000−2i2i00000000000000002i2i−2i−2i000000000000-2200
χ32222-2-2-22-222-22-222-22-2-2-2−2i2i−2i2i00002-2−2i−2i2i2i2-20000000000−2i2i0000000000000000−2i−2i2i2i0000000000002-200
χ33222-2-2-22-22-22-2222-22-2-2-22i−2i−2i2i2i2i−2i−2i-22−2i−2i2i2i-22000000002-22i−2i00002i2i−2i−2i22-2-2000000000000000000000000
χ34222-2-2-22-22-22-2222-22-2-2-22i−2i−2i2i−2i−2i2i2i-22−2i−2i2i2i-2200000000-222i−2i0000−2i−2i2i2i-2-222000000000000000000000000
χ35222-2-2-22-22-22-2222-22-2-2-2−2i2i2i−2i2i2i−2i−2i-222i2i−2i−2i-2200000000-22−2i2i00002i2i−2i−2i-2-222000000000000000000000000
χ36222-2-2-22-22-22-2222-22-2-2-2−2i2i2i−2i−2i−2i2i2i-222i2i−2i−2i-22000000002-2−2i2i0000−2i−2i2i2i22-2-2000000000000000000000000
χ37222-2-2-22-2-1-22-22-1-11-11112i−2i−2i2i2i2i−2i−2i1-1ii−i−i1-10000−i3−i3i3i32-2−ii33−3−3−i−iii-1-1110000000000−i3i33−30000000000
χ38222-2-2-22-2-1-22-22-1-11-11112i−2i−2i2i2i2i−2i−2i1-1ii−i−i1-10000i3i3−i3−i32-2−ii−3−333−i−iii-1-1110000000000i3−i3−330000000000
χ39222-2-2-22-2-1-22-22-1-11-11112i−2i−2i2i−2i−2i2i2i1-1ii−i−i1-10000−i3−i3i3i3-22−ii33−3−3ii−i−i11-1-10000000000i3−i3−330000000000
χ40222-2-2-22-2-1-22-22-1-11-11112i−2i−2i2i−2i−2i2i2i1-1ii−i−i1-10000i3i3−i3−i3-22−ii−3−333ii−i−i11-1-10000000000−i3i33−30000000000
χ41222-2-2-22-2-1-22-22-1-11-1111−2i2i2i−2i2i2i−2i−2i1-1−i−iii1-10000−i3−i3i3i3-22i−i−3−333−i−iii11-1-10000000000i3−i33−30000000000
χ42222-2-2-22-2-1-22-22-1-11-1111−2i2i2i−2i2i2i−2i−2i1-1−i−iii1-10000i3i3−i3−i3-22i−i33−3−3−i−iii11-1-10000000000−i3i3−330000000000
χ43222-2-2-22-2-1-22-22-1-11-1111−2i2i2i−2i−2i−2i2i2i1-1−i−iii1-10000−i3−i3i3i32-2i−i−3−333ii−i−i-1-1110000000000−i3i3−330000000000
χ44222-2-2-22-2-1-22-22-1-11-1111−2i2i2i−2i−2i−2i2i2i1-1−i−iii1-10000i3i3−i3−i32-2i−i33−3−3ii−i−i-1-1110000000000i3−i33−30000000000
χ452-2-2-22-22222-2-22-2-2-222-2200000000-2200002-2002-2000000002-22-2000000002-22-2000000000000002-20000
χ462-2-2-22-22222-2-22-2-2-222-2200000000-2200002-2002-2000000002-22-200000000-22-2200000000000000-220000
χ472-2-2-22-22222-2-22-2-2-222-2200000000-2200002-200-2200000000-22-22000000002-22-200000000000000-220000
χ482-2-2-22-22222-2-22-2-2-222-2200000000-2200002-200-2200000000-22-2200000000-22-22000000000000002-20000
χ492-2-2-22-2222-222-2-2-2-222-22000000002-20000-222-2002-22-200000000000000002-2-220000000000002-2000000
χ502-2-2-22-2222-222-2-2-2-222-22000000002-20000-222-2002-22-20000000000000000-222-2000000000000-22000000
χ512-2-2-22-2222-222-2-2-2-222-22000000002-20000-22-2200-22-2200000000000000002-2-22000000000000-22000000
χ522-2-2-22-2222-222-2-2-2-222-22000000002-20000-22-2200-22-220000000000000000-222-20000000000002-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222222220000000000-2-2000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022-2-2-2-222000000000022000000000000000000000000000000000000
χ55444-4-4-44-4-24-44-4-2-22-22224i−4i4i−4i0000-22−2i−2i2i2i-220000000000−2i2i000000000000000000000000000000000000
χ56444-4-4-44-4-24-44-4-2-22-2222−4i4i−4i4i0000-222i2i−2i−2i-2200000000002i−2i000000000000000000000000000000000000
χ5744-444-4-4-4400004-4-4-444-400000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ5844-444-4-4-4400004-4-4-444-4000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5944-4-4-44-44400004-44-4-4-440000000000000000000000000000000000000000000022−22−22220000000000000000
χ6044-4-4-44-44400004-44-4-4-4400000000000000000000000000000000000000000000−222222−220000000000000000
χ614-444-4-4-4440000-44-4-4-444000022−2222−2200000000000000000000000022−2222−220000000000000000000000000000
χ624-444-4-4-4440000-44-4-4-4440000−2222−2222000000000000000000000000−2222−22220000000000000000000000000000
χ634-444-4-4-44-200002-2222-2-2000022−2222−2200−2i32i3−2i32i3000000000000000000−22−22i6−i6i6−i6000000000000000000000000
χ644-444-4-4-44-200002-2222-2-2000022−2222−22002i3−2i32i3−2i3000000000000000000−22−22−i6i6−i6i6000000000000000000000000
χ654-444-4-4-44-200002-2222-2-20000−2222−222200−2i32i3−2i32i30000000000000000002−22−2−i6i6−i6i6000000000000000000000000
χ664-444-4-4-44-200002-2222-2-20000−2222−2222002i3−2i32i3−2i30000000000000000002−22−2i6−i6i6−i6000000000000000000000000
χ674-44-444-4-440000-444-44-4-40000−2i22i22i2−2i2000000000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ684-44-444-4-440000-444-44-4-400002i2−2i2−2i22i20000000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ694-44-444-4-4-200002-2-22-2220000−2i22i22i2−2i20023−23−2323000000000000000000i2−i2−i2i2i6−i6−i6i6000000000000000000000000
χ704-44-444-4-4-200002-2-22-2220000−2i22i22i2−2i200−232323−23000000000000000000i2−i2−i2i2−i6i6i6−i6000000000000000000000000
χ714-44-444-4-4-200002-2-22-22200002i2−2i2−2i22i20023−23−2323000000000000000000−i2i2i2−i2−i6i6i6−i6000000000000000000000000
χ724-44-444-4-4-200002-2-22-22200002i2−2i2−2i22i200−232323−23000000000000000000−i2i2i2−i2i6−i6−i6i6000000000000000000000000
χ734-4-44-444-4444-4-4-4-444-44-400000000-4-4000044000000000000000000000000000000000000000000000000
χ744-4-44-444-44-4-444-4-444-44-400000000440000-4-4000000000000000000000000000000000000000000000000
χ754-4-44-444-4-244-4-422-2-22-2200000000220000-2-20000−2i32i32i3−2i30000000000000000000000000000000000000000
χ764-4-44-444-4-244-4-422-2-22-2200000000220000-2-200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ774-4-44-444-4-2-4-44422-2-22-2200000000-2-200002200000000000023−23−232300000000000000000000000000000000
χ784-4-44-444-4-2-4-44422-2-22-2200000000-2-2000022000000000000−232323−2300000000000000000000000000000000
χ794-4-4-44-444-24-4-44222-2-22-2000000002-20000-22004-400000000-22-2200000000000000000000000000000000
χ804-4-4-44-444-24-4-44222-2-22-2000000002-20000-2200-44000000002-22-200000000000000000000000000000000
χ814-4-4-44-444-2-444-4222-2-22-200000000-2200002-24-400-22-220000000000000000000000000000000000000000
χ824-4-4-44-444-2-444-4222-2-22-200000000-2200002-2-44002-22-20000000000000000000000000000000000000000
χ8388-888-8-8-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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