Finite Group Databasebeta

← Group #10846323

Character table — Group #10846323

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212224466668888121212121212242424242424242488888888246612122444444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-111-1-11-1-11
χ10111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-11-1-111-111-1
χ11111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1111-1-1-111-1
χ12111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1-1111-1-11
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-1111-1-1-1111-11-1
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-111-1111-1-1-11-11
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-11-1-111-11-11
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-111-1-11-11-1
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-2000000000000-2-2000000000000000000000000002-20000-2200
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-2000000000000-2-200000000000000000000000000-2200002-200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000220000-2-200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000-2-200002200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-11111111111110000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-1-1-1-122-2-2111111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-1-1-1-1-2-2221111111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-222111122-2-211-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-2221111-2-22211-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ29222-2-2-22-222i2i−2i−2i2-2-2222-22-2-2-22i−2i2-22i2i−2i−2i2-20000000000002i−2i0000000000002i2i−2i−2i22-2-20000000000000000
χ30222-2-2-22-222i2i−2i−2i2-2-2222-22-2-2-22i−2i2-22i2i−2i−2i2-20000000000002i−2i000000000000−2i−2i2i2i-2-2220000000000000000
χ31222-2-2-22-222i2i−2i−2i-222-222-22-2-2-2−2i2i-222i2i−2i−2i-22000000002-22i−2i−2i2i000022-2-22i2i−2i−2i000000000000000000000000
χ32222-2-2-22-222i2i−2i−2i-222-222-22-2-2-2−2i2i-222i2i−2i−2i-2200000000-22−2i2i−2i2i0000-2-222−2i−2i2i2i000000000000000000000000
χ33222-2-2-22-22−2i−2i2i2i2-2-2222-22-2-2-2−2i2i2-2−2i−2i2i2i2-2000000000000−2i2i0000000000002i2i−2i−2i-2-2220000000000000000
χ34222-2-2-22-22−2i−2i2i2i2-2-2222-22-2-2-2−2i2i2-2−2i−2i2i2i2-2000000000000−2i2i000000000000−2i−2i2i2i22-2-20000000000000000
χ35222-2-2-22-22−2i−2i2i2i-222-222-22-2-2-22i−2i-22−2i−2i2i2i-22000000002-2−2i2i2i−2i000022-2-2−2i−2i2i2i000000000000000000000000
χ36222-2-2-22-22−2i−2i2i2i-222-222-22-2-2-22i−2i-22−2i−2i2i2i-2200000000-222i−2i2i−2i0000-2-2222i2i−2i−2i000000000000000000000000
χ37222-2-2-22-2-12i2i−2i−2i-222-2-1-11-1111−2i2i1-1−i−iii1-10000−i3−i3i3i32-22i−2ii−i33−3−3-1-111−i−iii0000000000−i3i33−30000000000
χ38222-2-2-22-2-12i2i−2i−2i-222-2-1-11-1111−2i2i1-1−i−iii1-10000−i3−i3i3i3-22−2i2ii−i33−3−311-1-1ii−i−i0000000000i3−i3−330000000000
χ39222-2-2-22-2-12i2i−2i−2i-222-2-1-11-1111−2i2i1-1−i−iii1-10000i3i3−i3−i32-22i−2ii−i−3−333-1-111−i−iii0000000000i3−i3−330000000000
χ40222-2-2-22-2-12i2i−2i−2i-222-2-1-11-1111−2i2i1-1−i−iii1-10000i3i3−i3−i3-22−2i2ii−i−3−33311-1-1ii−i−i0000000000−i3i33−30000000000
χ41222-2-2-22-2-1−2i−2i2i2i-222-2-1-11-11112i−2i1-1ii−i−i1-10000−i3−i3i3i32-2−2i2i−ii−3−333-1-111ii−i−i0000000000−i3i3−330000000000
χ42222-2-2-22-2-1−2i−2i2i2i-222-2-1-11-11112i−2i1-1ii−i−i1-10000−i3−i3i3i3-222i−2i−ii−3−33311-1-1−i−iii0000000000i3−i33−30000000000
χ43222-2-2-22-2-1−2i−2i2i2i-222-2-1-11-11112i−2i1-1ii−i−i1-10000i3i3−i3−i32-2−2i2i−ii33−3−3-1-111ii−i−i0000000000i3−i33−30000000000
χ44222-2-2-22-2-1−2i−2i2i2i-222-2-1-11-11112i−2i1-1ii−i−i1-10000i3i3−i3−i3-222i−2i−ii33−3−311-1-1−i−iii0000000000−i3i3−330000000000
χ452-2-22-222-220000-2-222-2-2-222-2200-2200002-2002-200000000002-22-20000000000002-22-2000000002-2000000
χ462-2-22-222-220000-2-222-2-2-222-2200-2200002-2002-200000000002-22-2000000000000-22-2200000000-22000000
χ472-2-22-222-220000-2-222-2-2-222-2200-2200002-200-220000000000-22-220000000000002-22-200000000-22000000
χ482-2-22-222-220000-2-222-2-2-222-2200-2200002-200-220000000000-22-22000000000000-22-22000000002-2000000
χ492-2-2-22-22220000-22-22-2-222-22-200-2-20000222-2002-22-200000000000000000000002-2-2200000000002-20000
χ502-2-2-22-22220000-22-22-2-222-22-200-2-20000222-2002-22-20000000000000000000000-222-20000000000-220000
χ512-2-2-22-22220000-22-22-2-222-22-200-2-2000022-2200-22-2200000000000000000000002-2-220000000000-220000
χ522-2-2-22-22220000-22-22-2-222-22-200-2-2000022-2200-22-220000000000000000000000-222-200000000002-20000
χ5344444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000022000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ55444-4-4-44-4-24i4i−4i−4i4-4-44-2-22-22224i−4i-22−2i−2i2i2i-22000000000000−2i2i000000000000000000000000000000000000
χ56444-4-4-44-4-2−4i−4i4i4i4-4-44-2-22-2222−4i4i-222i2i−2i−2i-220000000000002i−2i000000000000000000000000000000000000
χ5744-444-4-4-44000000004-44-4-4-44000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ5844-444-4-4-44000000004-44-4-4-440000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5944-4-4-44-444000000004-4-4-444-400000000000000000000000000000000000022−22−222200000000000000000000
χ6044-4-4-44-444000000004-4-4-444-4000000000000000000000000000000000000−222222−2200000000000000000000
χ614-444-4-4-4444-44-40000-44-4-4-44400004-44-40000000000000000000000000000000000000000000000000000
χ624-444-4-4-444-44-440000-44-4-4-4440000-44-440000000000000000000000000000000000000000000000000000
χ634-444-4-4-44-24-44-400002-2222-2-20000-22-2200000000000000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ644-444-4-4-44-24-44-400002-2222-2-20000-22-2200000000000000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ654-444-4-4-44-2-44-4400002-2222-2-200002-22-200000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ664-444-4-4-44-2-44-4400002-2222-2-200002-22-200000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ674-44-444-4-444i−4i−4i4i0000-444-44-4-400004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ684-44-444-4-44−4i4i4i−4i0000-444-44-4-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ694-44-444-4-4-24i−4i−4i4i00002-2-22-2220000−2i2i2i−2i00000000000000000000i6−i6−i6i6−666−6000000000000000000000000
χ704-44-444-4-4-24i−4i−4i4i00002-2-22-2220000−2i2i2i−2i00000000000000000000−i6i6i6−i66−6−66000000000000000000000000
χ714-44-444-4-4-2−4i4i4i−4i00002-2-22-22200002i−2i−2i2i00000000000000000000i6−i6−i6i66−6−66000000000000000000000000
χ724-44-444-4-4-2−4i4i4i−4i00002-2-22-22200002i−2i−2i2i00000000000000000000−i6i6i6−i6−666−6000000000000000000000000
χ734-4-44-444-44000044-4-4-4-4-444-44004-40000-4400000000000000000000000000000000000000000000000000
χ744-4-44-444-4-2000044-4-4222-2-22-200-2200002-20000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ754-4-44-444-4-2000044-4-4222-2-22-200-2200002-200002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ764-4-44-444-4-20000-4-444222-2-22-2002-20000-22004-40000000000-22-2200000000000000000000000000000000
χ774-4-44-444-4-20000-4-444222-2-22-2002-20000-2200-4400000000002-22-200000000000000000000000000000000
χ784-4-4-44-444400004-44-4-4-444-44-400440000-4-400000000000000000000000000000000000000000000000000
χ794-4-4-44-444-200004-44-422-2-22-2200-2-20000220000000000000023−23−232300000000000000000000000000000000
χ804-4-4-44-444-200004-44-422-2-22-2200-2-200002200000000000000−232323−2300000000000000000000000000000000
χ814-4-4-44-444-20000-44-4422-2-22-2200220000-2-24-400-22-22000000000000000000000000000000000000000000
χ824-4-4-44-444-20000-44-4422-2-22-2200220000-2-2-44002-22-2000000000000000000000000000000000000000000
χ8388-888-8-8-8-400000000-44-4444-4000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-400000000-4444-4-44000000000000000000000000000000000000000000000000000000000000

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