Finite Group Databasebeta

← Group #10828468

Character table — Group #10828468

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order12222222344444444666666622121212121212121244442244444466888812121212121212122424242424242424444444661212224444448888
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
χ311111111111111111111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ71111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1
χ10111111111-1-1-1-111111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111
χ11111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ12111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-11111-1-1-1-111-1-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111111-1-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-2222200000000-2-200000000000000000000-2-222-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-200000000-2-20000000000000000000022-2-2220000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22222000000002200000000000000000000-2-2-2-2220000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022000000000000000000002222-2-20000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022-2-222-2-2-1-1-2-2-2-21111111111111111000000-1-1-1-1000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-222-2-222-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000001111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-10000001111000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-100002222-2-2-2-21122-2-2-1-1-1-11111-1-1-1-11111000000-1-111000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1000022-2-2-2-22211-2-2221111-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-22222-2-211-2-222-1-1-1-111111111-1-1-1-100000011-1-1000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-2-2-222221122-2-21111-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ2922-2-22-22-222i2i−2i−2i000022-2-22-2-200002i2i−2i−2i002i2i−2i−2i00000000002−2−i2i20000000022−2−2−i2−i2i2i2002-200000000000000−i2i22−2
χ3022-2-22-22-222i2i−2i−2i000022-2-22-2-200002i2i−2i−2i002i2i−2i−2i0000000000−22i2−i200000000−2−222i2i2−i2−i2002-200000000000000i2−i2−22
χ3122-2-22-22-222i2i−2i−2i000022-2-22-2-200002i2i−2i−2i00−2i−2i2i2i00000000002−2−i2i20000000022−2−2−i2−i2i2i200-2200000000000000i2−i2−22
χ3222-2-22-22-222i2i−2i−2i000022-2-22-2-200002i2i−2i−2i00−2i−2i2i2i0000000000−22i2−i200000000−2−222i2i2−i2−i200-2200000000000000−i2i22−2
χ3322-2-22-22-22−2i−2i2i2i000022-2-22-2-20000−2i−2i2i2i002i2i−2i−2i00000000002−2i2−i20000000022−2−2i2i2−i2−i200-2200000000000000−i2i2−22
χ3422-2-22-22-22−2i−2i2i2i000022-2-22-2-20000−2i−2i2i2i002i2i−2i−2i0000000000−22−i2i200000000−2−222−i2−i2i2i200-2200000000000000i2−i22−2
χ3522-2-22-22-22−2i−2i2i2i000022-2-22-2-20000−2i−2i2i2i00−2i−2i2i2i00000000002−2i2−i20000000022−2−2i2i2−i2−i2002-200000000000000i2−i22−2
χ3622-2-22-22-22−2i−2i2i2i000022-2-22-2-20000−2i−2i2i2i00−2i−2i2i2i0000000000−22−i2i200000000−2−222−i2−i2i2i2002-200000000000000−i2i2−22
χ372-2-2222-2-2200002-22-22-22-2-22-2002-200002-22i−2i2i−2i0000002i−2i00000000002i2i−2i−2i000000002i−2i0000000000002-2000000
χ382-2-2222-2-2200002-22-22-22-2-22-2002-200002-22i−2i2i−2i000000−2i2i0000000000−2i−2i2i2i000000002i−2i000000000000-22000000
χ392-2-2222-2-2200002-22-22-22-2-22-2002-200002-2−2i2i−2i2i0000002i−2i00000000002i2i−2i−2i00000000−2i2i000000000000-22000000
χ402-2-2222-2-2200002-22-22-22-2-22-2002-200002-2−2i2i−2i2i000000−2i2i0000000000−2i−2i2i2i00000000−2i2i0000000000002-2000000
χ412-2-2222-2-220000-22-222-22-2-22-200-220000-222i−2i2i−2i002i−2i00000000002i2i−2i−2i000000000000−2i2i00000000002-200000000
χ422-2-2222-2-220000-22-222-22-2-22-200-220000-222i−2i2i−2i00−2i2i0000000000−2i−2i2i2i000000000000−2i2i0000000000-2200000000
χ432-2-2222-2-220000-22-222-22-2-22-200-220000-22−2i2i−2i2i002i−2i00000000002i2i−2i−2i0000000000002i−2i0000000000-2200000000
χ442-2-2222-2-220000-22-222-22-2-22-200-220000-22−2i2i−2i2i00−2i2i0000000000−2i−2i2i2i0000000000002i−2i00000000002-200000000
χ452-2-22-2-22222-22-222-2-2-2-2-2-22222-2-2-22-22-22200002-2002-2002-2000000000000000000000000002-22-2000000000000
χ462-2-22-2-22222-22-222-2-2-2-2-2-22222-2-2-22-22-2220000-2200-22002-200000000000000000000000000-22-22000000000000
χ472-2-22-2-22222-22-2-2-222-2-2-2-2222-22222-22-2-2-2000000000000-220000000000000000000000000000002-200002-20000
χ482-2-22-2-22222-22-2-2-222-2-2-2-2222-22222-22-2-2-2000000000000-22000000000000000000000000000000-220000-220000
χ492-2-22-2-2222-22-2222-2-2-2-2-2-2222-22-2-2-22-222200002-200-2200-22000000000000000000000000002-2-22000000000000
χ502-2-22-2-2222-22-2222-2-2-2-2-2-2222-22-2-2-22-22220000-22002-200-2200000000000000000000000000-222-2000000000000
χ512-2-22-2-2222-22-22-2-222-2-2-2-22222-222-22-22-2-20000000000002-20000000000000000000000000000002-20000-220000
χ522-2-22-2-2222-22-22-2-222-2-2-2-22222-222-22-22-2-20000000000002-2000000000000000000000000000000-2200002-20000
χ532-2-22-2-222-12-22-222-2-21111-1-1-12-211-11-11-1-100002-2002-200-110000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000-11-11000000000000
χ542-2-22-2-222-12-22-222-2-21111-1-1-12-211-11-11-1-100002-2002-200-110000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000-11-11000000000000
χ552-2-22-2-222-12-22-222-2-21111-1-1-12-211-11-11-1-10000-2200-2200-110000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000001-11-1000000000000
χ562-2-22-2-222-12-22-222-2-21111-1-1-12-211-11-11-1-10000-2200-2200-110000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000001-11-1000000000000
χ572-2-22-2-222-1-22-2222-2-21111-1-1-1-22111-11-1-1-100002-200-22001-10000−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3000000-111-1000000000000
χ582-2-22-2-222-1-22-2222-2-21111-1-1-1-22111-11-1-1-100002-200-22001-10000i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3000000-111-1000000000000
χ592-2-22-2-222-1-22-2222-2-21111-1-1-1-22111-11-1-1-10000-22002-2001-10000−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000001-1-11000000000000
χ602-2-22-2-222-1-22-2222-2-21111-1-1-1-22111-11-1-1-10000-22002-2001-10000i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000001-1-11000000000000
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
χ634444-4-4-4-4400004-4-44-44-44-44-400-4400004-400000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-440000-444-4-44-44-44-4004-40000-4400000000000000000000000000000000000000000000000000000000
χ654444-4-4-4-4-200004-4-442-22-22-22002-20000-22000000000000000000000023−23−2323000000000000000000000000000000
χ664444-4-4-4-4-200004-4-442-22-22-22002-20000-220000000000000000000000−232323−23000000000000000000000000000000
χ674444-4-4-4-4-20000-444-42-22-22-2200-2200002-200000000000000000023−23−23230000000000000000000000000000000000
χ684444-4-4-4-4-20000-444-42-22-22-2200-2200002-2000000000000000000−232323−230000000000000000000000000000000000
χ6944-4-44-44-4-24i4i−4i−4i0000-2-222-2220000−2i−2i2i2i000000000000000022−22−2i22i200000000−2−222i2i2−i2−i20000000000000000000000
χ7044-4-44-44-4-24i4i−4i−4i0000-2-222-2220000−2i−2i2i2i0000000000000000−22222i2−2i20000000022−2−2−i2−i2i2i20000000000000000000000
χ7144-4-44-44-4-2−4i−4i4i4i0000-2-222-22200002i2i−2i−2i000000000000000022−222i2−2i200000000−2−222−i2−i2i2i20000000000000000000000
χ7244-4-44-44-4-2−4i−4i4i4i0000-2-222-22200002i2i−2i−2i0000000000000000−2222−2i22i20000000022−2−2i2i2−i2−i20000000000000000000000
χ7344-4-4-44-44400000000-444-4-4-440000000000000000000000000000000000000000000000004-40000000000000000
χ7444-4-4-44-44400000000-444-4-4-44000000000000000000000000000000000000000000000000-440000000000000000
χ754-44-44-4-444000000004-4-44-4-4400000000004-4-440000000000000000000000000000000000000000000000000000
χ764-44-44-4-444000000004-4-44-4-440000000000-444-40000000000000000000000000000000000000000000000000000
χ774-44-4-444-444i−4i−4i4i0000-4-4444-4-400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ784-44-4-444-44−4i4i4i−4i0000-4-4444-4-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ794-44-4-444-4-24i−4i−4i4i000022-2-2-2220000−2i2i2i−2i0000000000000000000000000000i6−i6−i6i66−6−660000000000000000000000
χ804-44-4-444-4-24i−4i−4i4i000022-2-2-2220000−2i2i2i−2i0000000000000000000000000000−i6i6i6−i6−666−60000000000000000000000
χ814-44-4-444-4-2−4i4i4i−4i000022-2-2-22200002i−2i−2i2i0000000000000000000000000000i6−i6−i6i6−666−60000000000000000000000
χ824-44-4-444-4-2−4i4i4i−4i000022-2-2-22200002i−2i−2i2i0000000000000000000000000000−i6i6i6−i66−6−660000000000000000000000
χ834-4-4444-4-4-200004-44-4-22-222-2200-220000-2200000000004i−4i0000000000−2i−2i2i2i000000000000000000000000000000
χ844-4-4444-4-4-200004-44-4-22-222-2200-220000-220000000000−4i4i00000000002i2i−2i−2i000000000000000000000000000000
χ854-4-4444-4-4-20000-44-44-22-222-22002-200002-20000004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000000
χ864-4-4444-4-4-20000-44-44-22-222-22002-200002-2000000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000000
χ874-4-44-4-444-24-44-4-4-4442222-2-2-2-44-2-2-22-22220000000000002-2000000000000000000000000000000000000000000
χ884-4-44-4-444-2-44-44-4-4442222-2-2-24-4-2-22-22-222000000000000-22000000000000000000000000000000000000000000
χ8988-8-8-88-88-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-88-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000

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