Finite Group Databasebeta

← Group #10846321

Character table — Group #10846321

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222222234444444466666664412121212121212122224444466666612121212121212121212121288888888246612124444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-11111-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-111111111111-1-11111-1-1-1-1111-1-1-11-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-111-1-11-1
χ10111111111-1-1-1-111111111111-1-11111-1-1-1-1111-1-1-11-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-111-11
χ11111111111-1-1-1-111111111111-1-11111-1-1-1-111-11-1-1-111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-111-1-111-1-1-1-111-11
χ12111111111-1-1-1-111111111111-1-11111-1-1-1-111-11-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-11111-1-11-1
χ13111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-11-1111-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11-111-1-1-1-11111-1-1-11
χ14111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-11-1111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111-111-1-111-1-1-1-1111-1
χ15111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-11-1-111-1-111-1-1111-1
χ16111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-11-1-11111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-2-2-2-2-22222002-200-22000022-2-2-2-2-2-2000022000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2222200-22002-20000-2-2-2-222220000-2-2000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2002200-2-20000222222-2-20000-2-2000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200-2-200220000-2-222-2-222000022000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-111-1-11111-1-1-1-11100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1-1-1-1-11111-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111-1-111111111110000000022-1-1-1-10000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1002-200-22−i3−i3i3i3-1-1111111−i3−i3i3i3-1-10000000000−i3i3−i3i30000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1002-200-22i3i3−i3−i3-1-1111111i3i3−i3−i3-1-10000000000i3−i3i3−i30000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-100-22002-2−i3−i3i3i31111-1-1-1-1−i3−i3i3i3110000000000i3−i3i3−i30000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-100-22002-2i3i3−i3−i31111-1-1-1-1i3i3−i3−i3110000000000−i3i3−i3i30000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-1-11111222-2-2-22-2-1-1-1-1-1-11111-1-111111100000000-2211-1-10000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-1-1111122-22-2-2-22-1-1-1-11111-1-1111111-1-1000000002-2-1-1110000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-22-2222-21111-1-11111-1-1-1-1-1-111000000002-2-1-1110000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-2-2222-2211111111-1-111-1-1-1-1-1-100000000-2211-1-10000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111002200-2-2−i3−i3i3i3-1-1-1-1-1-111i3i3−i3−i3110000000000i3−i3−i3i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111002200-2-2i3i3−i3−i3-1-1-1-1-1-111−i3−i3i3i3110000000000−i3i3i3−i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100-2-20022−i3−i3i3i311-1-111-1-1i3i3−i3−i3-1-10000000000−i3i3i3−i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100-2-20022i3i3−i3−i311-1-111-1-1−i3−i3i3i3-1-10000000000i3−i3−i3i30000000000
χ37222-2-2-22-222i2i−2i−2i2-2-2222-2-22-2-22i−2i22-2-22i2i−2i−2i000000000000002i−2i00000000002i2i−2i−2i22-2-20000000000000000
χ38222-2-2-22-222i2i−2i−2i2-2-2222-2-22-2-22i−2i22-2-22i2i−2i−2i000000000000002i−2i0000000000−2i−2i2i2i-2-2220000000000000000
χ39222-2-2-22-222i2i−2i−2i-222-222-2-22-2-2−2i2i-2-2222i2i−2i−2i00000000000000−2i2i00000000000000000000000000002-22i−2i00
χ40222-2-2-22-222i2i−2i−2i-222-222-2-22-2-2−2i2i-2-2222i2i−2i−2i00000000000000−2i2i0000000000000000000000000000-22−2i2i00
χ41222-2-2-22-22−2i−2i2i2i2-2-2222-2-22-2-2−2i2i22-2-2−2i−2i2i2i00000000000000−2i2i00000000002i2i−2i−2i-2-2220000000000000000
χ42222-2-2-22-22−2i−2i2i2i2-2-2222-2-22-2-2−2i2i22-2-2−2i−2i2i2i00000000000000−2i2i0000000000−2i−2i2i2i22-2-20000000000000000
χ43222-2-2-22-22−2i−2i2i2i-222-222-2-22-2-22i−2i-2-222−2i−2i2i2i000000000000002i−2i00000000000000000000000000002-2−2i2i00
χ44222-2-2-22-22−2i−2i2i2i-222-222-2-22-2-22i−2i-2-222−2i−2i2i2i000000000000002i−2i0000000000000000000000000000-222i−2i00
χ452-2-22-2-22220000-22-22-2-22-222-2002-22-200002-20000002-22-20000000000000000002-22-2000000002-2000000
χ462-2-22-2-22220000-22-22-2-22-222-2002-22-200002-20000002-22-2000000000000000000-22-2200000000-22000000
χ472-2-22-2-22220000-22-22-2-22-222-2002-22-20000-22000000-22-220000000000000000002-22-200000000-22000000
χ482-2-22-2-22220000-22-22-2-22-222-2002-22-20000-22000000-22-22000000000000000000-22-22000000002-2000000
χ492-2-2-2222-220000-2-222-2-2-222-22002-2-22000000002-2000000000000002-22-20000002-2-220000002-200000000
χ502-2-2-2222-220000-2-222-2-2-222-22002-2-22000000002-2000000000000002-22-2000000-222-2000000-2200000000
χ512-2-2-2222-220000-2-222-2-2-222-22002-2-2200000000-2200000000000000-22-220000002-2-22000000-2200000000
χ522-2-2-2222-220000-2-222-2-2-222-22002-2-2200000000-2200000000000000-22-22000000-222-20000002-200000000
χ53444-4-4-44-4-24i4i−4i−4i4-4-44-2-222-2224i−4i-2-222−2i−2i2i2i00000000000000−2i2i0000000000000000000000000000000000
χ54444-4-4-44-4-24i4i−4i−4i-444-4-2-222-222−4i4i22-2-2−2i−2i2i2i000000000000002i−2i0000000000000000000000000000000000
χ55444-4-4-44-4-2−4i−4i4i4i4-4-44-2-222-222−4i4i-2-2222i2i−2i−2i000000000000002i−2i0000000000000000000000000000000000
χ56444-4-4-44-4-2−4i−4i4i4i-444-4-2-222-2224i−4i22-2-22i2i−2i−2i00000000000000−2i2i0000000000000000000000000000000000
χ5744-444-4-4-44000000004-44-4-4-44000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ5844-444-4-4-44000000004-44-4-4-440000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5944-4-4-44-444000000004-4-44-44-400000000000000000000000000000000000022−22−222200000000000000000000
χ6044-4-4-44-444000000004-4-44-44-4000000000000000000000000000000000000−222222−2200000000000000000000
χ614-444-44-4-444i−4i4i−4i0000-4444-4-4-40000004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ624-444-44-4-44−4i4i−4i4i0000-4444-4-4-4000000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ634-444-44-4-4-24i−4i4i−4i00002-2-2-2222000000−2i2i−2i2i0000000000000000−2i32i323−23000000000000000000000000000000
χ644-444-44-4-4-24i−4i4i−4i00002-2-2-2222000000−2i2i−2i2i00000000000000002i3−2i3−2323000000000000000000000000000000
χ654-444-44-4-4-2−4i4i−4i4i00002-2-2-22220000002i−2i2i−2i0000000000000000−2i32i3−2323000000000000000000000000000000
χ664-444-44-4-4-2−4i4i−4i4i00002-2-2-22220000002i−2i2i−2i00000000000000002i3−2i323−23000000000000000000000000000000
χ674-44-44-4-4444-4-440000-44-4-4-4440000004-4-4400000000000000000000000000000000000000000000000000
χ684-44-44-4-444-444-40000-44-4-4-444000000-444-400000000000000000000000000000000000000000000000000
χ694-44-44-4-44-24-4-4400002-2222-2-2000000-222-2000000000000−2i32i30000000000−2i32i3000000000000000000000000
χ704-44-44-4-44-24-4-4400002-2222-2-2000000-222-20000000000002i3−2i300000000002i3−2i3000000000000000000000000
χ714-44-44-4-44-2-444-400002-2222-2-20000002-2-22000000000000−2i32i300000000002i3−2i3000000000000000000000000
χ724-44-44-4-44-2-444-400002-2222-2-20000002-2-220000000000002i3−2i30000000000−2i32i3000000000000000000000000
χ734-4-44-4-444400004-44-4-4-44-444-400-44-44000000000000000000000000000000000000000000000000000000
χ744-4-44-4-444-200004-44-422-22-2-22002-22-2000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ754-4-44-4-444-200004-44-422-22-2-22002-22-20000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ764-4-44-4-444-20000-44-4422-22-2-2200-22-2200004-4000000-22-2200000000000000000000000000000000000000
χ774-4-44-4-444-20000-44-4422-22-2-2200-22-220000-440000002-22-200000000000000000000000000000000000000
χ784-4-4-4444-44000044-4-4-4-4-444-4400-444-4000000000000000000000000000000000000000000000000000000
χ794-4-4-4444-4-2000044-4-4222-2-22-2002-2-22000000000000000000000000−2i32i32i3−2i300000000000000000000000000
χ804-4-4-4444-4-2000044-4-4222-2-22-2002-2-220000000000000000000000002i3−2i3−2i32i300000000000000000000000000
χ814-4-4-4444-4-20000-4-444222-2-22-200-222-2000000004-400000000000000-22-2200000000000000000000000000
χ824-4-4-4444-4-20000-4-444222-2-22-200-222-200000000-44000000000000002-22-200000000000000000000000000
χ8388-888-8-8-8-400000000-44-4444-4000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000

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