Finite Group Databasebeta

← Group #10826941

Character table — Group #10826941

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order1222222234444444466666662212121212121212122222222244446666668888121212122424242424242424224444661212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ10111111111-1-1-1-111111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-111-1-111-1-1-1-111
χ11111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-111
χ12111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-111-1-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-2222200000000-2-200000000000000000000-2-2-2-2220000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-200000000-2-2000000000000000000002222-2-20000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2222200000000220000000000000000000022-2-2-2-20000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002200000000000000000000-2-222220000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022-2-222-2-2-1-11111-2-2-2-2111111111111000000-1-1-1-1000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-222-2-222-1-1-1-1-1-1-2-2-2-2-1-1-1-1111111110000001111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-1111122221111-1-1-1-1-1-1-1-10000001111000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-100002222-2-2-2-211-1-1-1-122-2-21111-1-1-1-11111000000-1-111000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1000022-2-2-2-222111111-2-222-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-22222-2-211-1-1-1-1-2-22211111111-1-1-1-100000011-1-1000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-2-2-2222211111122-2-2-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ29222-22-2-2-222i2i−2i−2i0000222-2-2-2-200002i2i−2i−2i0022-2-2000000000000002−2−i2i2000022−2−2−i2−i2i2i200002i−2i0000000000002−2−i2i2
χ30222-22-2-2-222i2i−2i−2i0000222-2-2-2-200002i2i−2i−2i0022-2-200000000000000−22i2−i20000−2−222i2i2−i2−i200002i−2i000000000000−22i2−i2
χ31222-22-2-2-222i2i−2i−2i0000222-2-2-2-200002i2i−2i−2i00-2-222000000000000002−2−i2i2000022−2−2−i2−i2i2i20000−2i2i000000000000−22i2−i2
χ32222-22-2-2-222i2i−2i−2i0000222-2-2-2-200002i2i−2i−2i00-2-22200000000000000−22i2−i20000−2−222i2i2−i2−i20000−2i2i0000000000002−2−i2i2
χ33222-22-2-2-22−2i−2i2i2i0000222-2-2-2-20000−2i−2i2i2i0022-2-2000000000000002−2i2−i2000022−2−2i2i2−i2−i20000−2i2i0000000000002−2i2−i2
χ34222-22-2-2-22−2i−2i2i2i0000222-2-2-2-20000−2i−2i2i2i0022-2-200000000000000−22−i2i20000−2−222−i2−i2i2i20000−2i2i000000000000−22−i2i2
χ35222-22-2-2-22−2i−2i2i2i0000222-2-2-2-20000−2i−2i2i2i00-2-222000000000000002−2i2−i2000022−2−2i2i2−i2−i200002i−2i000000000000−22−i2i2
χ36222-22-2-2-22−2i−2i2i2i0000222-2-2-2-20000−2i−2i2i2i00-2-22200000000000000−22−i2i20000−2−222−i2−i2i2i200002i−2i0000000000002−2i2−i2
χ3722-2-2-2-22222-22-222-2-22-2-2-2-2222-2-2-22-22-22200002-2002-2002-2000000000000000000000000002-22-2000000000000
χ3822-2-2-2-22222-22-222-2-22-2-2-2-2222-2-2-22-22-2220000-2200-22002-200000000000000000000000000-22-22000000000000
χ3922-2-2-2-22222-22-2-2-2222-2-2-2-222-22222-22-2-2-2000000000000-220000000000000000000000000000002-200002-20000
χ4022-2-2-2-22222-22-2-2-2222-2-2-2-222-22222-22-2-2-2000000000000-22000000000000000000000000000000-220000-220000
χ4122-2-2-2-2222-22-2222-2-22-2-2-2-222-22-2-2-22-222200002-200-2200-22000000000000000000000000002-2-22000000000000
χ4222-2-2-2-2222-22-2222-2-22-2-2-2-222-22-2-2-22-22220000-22002-200-2200000000000000000000000000-222-2000000000000
χ4322-2-2-2-2222-22-22-2-2222-2-2-2-2222-222-22-22-2-20000000000002-20000000000000000000000000000002-20000-220000
χ4422-2-2-2-2222-22-22-2-2222-2-2-2-2222-222-22-22-2-20000000000002-2000000000000000000000000000000-2200002-20000
χ4522-2-2-2-222-12-22-222-2-2-11111-1-12-211-11-11-1-100002-2002-200-11−i3−i3i3i30000−i3−i3i3i3−i3i3−i3i3−i3i3−i3i3000000-11-11000000000000
χ4622-2-2-2-222-12-22-222-2-2-11111-1-12-211-11-11-1-100002-2002-200-11i3i3−i3−i30000i3i3−i3−i3i3−i3i3−i3i3−i3i3−i3000000-11-11000000000000
χ4722-2-2-2-222-12-22-222-2-2-11111-1-12-211-11-11-1-10000-2200-2200-11−i3−i3i3i30000−i3−i3i3i3i3−i3i3−i3i3−i3i3−i30000001-11-1000000000000
χ4822-2-2-2-222-12-22-222-2-2-11111-1-12-211-11-11-1-10000-2200-2200-11i3i3−i3−i30000i3i3−i3−i3−i3i3−i3i3−i3i3−i3i30000001-11-1000000000000
χ4922-2-2-2-222-1-22-2222-2-2-11111-1-1-22111-11-1-1-100002-200-22001-1−i3−i3i3i30000i3i3−i3−i3−i3i3−i3i3i3−i3i3−i3000000-111-1000000000000
χ5022-2-2-2-222-1-22-2222-2-2-11111-1-1-22111-11-1-1-100002-200-22001-1i3i3−i3−i30000−i3−i3i3i3i3−i3i3−i3−i3i3−i3i3000000-111-1000000000000
χ5122-2-2-2-222-1-22-2222-2-2-11111-1-1-22111-11-1-1-10000-22002-2001-1−i3−i3i3i30000i3i3−i3−i3i3−i3i3−i3−i3i3−i3i30000001-1-11000000000000
χ5222-2-2-2-222-1-22-2222-2-2-11111-1-1-22111-11-1-1-10000-22002-2001-1i3i3−i3−i30000−i3−i3i3i3−i3i3−i3i3i3−i3i3−i30000001-1-11000000000000
χ532-2-2-222-22200002-22-2-22-22-2-22002-200002-22-22-20000002-200000000002-22-200000000002-200000000002-2000000
χ542-2-2-222-22200002-22-2-22-22-2-22002-200002-22-22-2000000-220000000000-22-2200000000002-20000000000-22000000
χ552-2-2-222-22200002-22-2-22-22-2-22002-200002-2-22-220000002-200000000002-22-20000000000-220000000000-22000000
χ562-2-2-222-22200002-22-2-22-22-2-22002-200002-2-22-22000000-220000000000-22-220000000000-2200000000002-2000000
χ572-2-2-222-2220000-22-22-22-22-2-2200-220000-222-22-2002-20000002-22-2000000000000000000-22000000002-200000000
χ582-2-2-222-2220000-22-22-22-22-2-2200-220000-222-22-200-22000000-22-22000000000000000000-2200000000-2200000000
χ592-2-2-222-2220000-22-22-22-22-2-2200-220000-22-22-22002-20000002-22-20000000000000000002-200000000-2200000000
χ602-2-2-222-2220000-22-22-22-22-2-2200-220000-22-22-2200-22000000-22-220000000000000000002-2000000002-200000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000000000
χ63444-44-4-4-4-24i4i−4i−4i0000-2-2-222220000−2i−2i2i2i0000000000000000000022−22−2i22i20000−2−222i2i2−i2−i20000000000000000000000
χ64444-44-4-4-4-24i4i−4i−4i0000-2-2-222220000−2i−2i2i2i00000000000000000000−22222i2−2i2000022−2−2−i2−i2i2i20000000000000000000000
χ65444-44-4-4-4-2−4i−4i4i4i0000-2-2-2222200002i2i−2i−2i0000000000000000000022−222i2−2i20000−2−222−i2−i2i2i20000000000000000000000
χ66444-44-4-4-4-2−4i−4i4i4i0000-2-2-2222200002i2i−2i−2i00000000000000000000−2222−2i22i2000022−2−2i2i2−i2−i20000000000000000000000
χ6744-44-44-4-444i−4i−4i4i00004-4-444-4-400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ6844-44-44-4-44−4i4i4i−4i00004-4-444-4-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ6944-44-44-4-4-24i−4i−4i4i0000-222-2-2220000−2i2i2i−2i0000000000000000000000000000i6−i6−i6i66−6−660000000000000000000000
χ7044-44-44-4-4-24i−4i−4i4i0000-222-2-2220000−2i2i2i−2i0000000000000000000000000000−i6i6i6−i6−666−60000000000000000000000
χ7144-44-44-4-4-2−4i4i4i−4i0000-222-2-22200002i−2i−2i2i0000000000000000000000000000i6−i6−i6i6−666−60000000000000000000000
χ7244-44-44-4-4-2−4i4i4i−4i0000-222-2-22200002i−2i−2i2i0000000000000000000000000000−i6i6i6−i66−6−660000000000000000000000
χ7344-4-4-4-444-24-44-4-4-444-22222-2-2-44-2-2-22-22220000000000002-2000000000000000000000000000000000000000000
χ7444-4-4-4-444-2-44-44-4-444-22222-2-24-4-2-22-22-222000000000000-22000000000000000000000000000000000000000000
χ754-444-4-4-44400004-4-44-4-44-44-4400-4400004-400000000000000000000000000000000000000000000000000000000
χ764-444-4-4-4440000-444-4-4-44-44-44004-40000-4400000000000000000000000000000000000000000000000000000000
χ774-444-4-4-44-200004-4-4422-22-22-2002-20000-220000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ784-444-4-4-44-200004-4-4422-22-22-2002-20000-2200000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ794-444-4-4-44-20000-444-422-22-22-200-2200002-200000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ804-444-4-4-44-20000-444-422-22-22-200-2200002-2000000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ814-44-4-444-4400000000-4-444-44-4000000000000000000000000000000000000000000004-400000000000000000000
χ824-44-4-444-4400000000-4-444-44-400000000000000000000000000000000000000000000-4400000000000000000000
χ834-4-444-44-4400000000-44-4-444-400000000004-4-440000000000000000000000000000000000000000000000000000
χ844-4-444-44-4400000000-44-4-444-40000000000-444-40000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-200004-44-42-22-222-200-220000-2200000000004-40000000000-22-22000000000000000000000000000000
χ864-4-4-444-44-200004-44-42-22-222-200-220000-220000000000-4400000000002-22-2000000000000000000000000000000
χ874-4-4-444-44-20000-44-442-22-222-2002-200002-20000004-4000000-22-2200000000000000000000000000000000000000
χ884-4-4-444-44-20000-44-442-22-222-2002-200002-2000000-440000002-22-200000000000000000000000000000000000000
χ898-88-8-888-8-40000000044-4-44-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000000000

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