Finite Group Databasebeta

← Group #10896524

Character table — Group #10896524

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order122222223444444446666666441212121212121212444444444444888812121212121212121212242424242424242444444412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ61111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ911111111111-1-1-1-1111111111-1-1111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1
χ1011111111111-1-1-1-1111111111-1-1111-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1-1-111
χ1111111111111-1-1-1-1111111111-1-1111-1-1-1-111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111
χ1211111111111-1-1-1-1111111111-1-1111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1311111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-11111-1-1
χ1511111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-111-1-1
χ1611111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ17222222222-2-22222-2-22222222-2-2-2-2-22222-22222000000000000-2-20000000000000000-2-2-2-2220000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-22222-2-2-2-2-2000000000000-2-200000000000000002222-2-20000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22222000000000000220000000000000000-2-222-2-20000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000022000000000000000022-2-2220000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022-2-222-2-2-2-2-2-2-1-11111111111111111000000-1-1-1-1000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000001111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000001111000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-100002222-2-2-2-222-2-211-1-1-1-11111-1-1-1-11111000000-1-111000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1000022-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-10000-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-100000011-1-1000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-10000-2-2-2-2222222-2-2111111-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ2922-22-2-2-2222-200002-2-22-2-22-22002-2-2000022i2i−2i−2i0000002-2000000000022-2-2000000002i−2i0000000000002i−2i000000
χ3022-22-2-2-2222-200002-2-22-2-22-22002-2-2000022i2i−2i−2i000000-220000000000-2-222000000002i−2i000000000000−2i2i000000
χ3122-22-2-2-2222-200002-2-22-2-22-22002-2-200002−2i−2i2i2i0000002-2000000000022-2-200000000−2i2i000000000000−2i2i000000
χ3222-22-2-2-2222-200002-2-22-2-22-22002-2-200002−2i−2i2i2i000000-220000000000-2-22200000000−2i2i0000000000002i−2i000000
χ3322-22-2-2-222-220000-22-22-2-22-2200-2220000-22i2i−2i−2i002i−2i00000000002i2i−2i−2i000000000000−2i2i000000000000002-20000
χ3422-22-2-2-222-220000-22-22-2-22-2200-2220000-22i2i−2i−2i00−2i2i0000000000−2i−2i2i2i000000000000−2i2i00000000000000-220000
χ3522-22-2-2-222-220000-22-22-2-22-2200-2220000-2−2i−2i2i2i002i−2i00000000002i2i−2i−2i0000000000002i−2i00000000000000-220000
χ3622-22-2-2-222-220000-22-22-2-22-2200-2220000-2−2i−2i2i2i00−2i2i0000000000−2i−2i2i2i0000000000002i−2i000000000000002-20000
χ3722-2-222-2-222222-2-2-2-2-2222-2-2-22-222-222-2-2-200000000000000002-2000000000000000000000000002-22-200000000
χ3822-2-222-2-222222-2-2-2-2-2222-2-2-22-222-222-2-2-200000000000000002-200000000000000000000000000-22-2200000000
χ3922-2-222-2-2222-2-222-2-2-2222-2-2-2-2222-2-2-222-20000000000000000-22000000000000000000000000002-2-2200000000
χ4022-2-222-2-2222-2-222-2-2-2222-2-2-2-2222-2-2-222-20000000000000000-2200000000000000000000000000-222-200000000
χ4122-2-222-2-22-2-222-2-222-2222-2-2-2-22-2-2222-2-2200002i−2i002i−2i000000-2200000000000000000000002i−2i2i−2i000000000000
χ4222-2-222-2-22-2-222-2-222-2222-2-2-2-22-2-2222-2-220000−2i2i00−2i2i000000-220000000000000000000000−2i2i−2i2i000000000000
χ4322-2-222-2-22-2-2-2-22222-2222-2-2-22-2-2-22-2-222200002i−2i00−2i2i0000002-200000000000000000000002i−2i−2i2i000000000000
χ4422-2-222-2-22-2-2-2-22222-2222-2-2-22-2-2-22-2-22220000−2i2i002i−2i0000002-20000000000000000000000−2i2i2i−2i000000000000
χ4522-2-222-2-2-1-2-222-2-2221-1-1-1111-2211-1-1-111-100002i−2i002i−2i0000001-13−33−33−33−3−i3−i3i3i3−i3−i3i3i3000000−ii−ii000000000000
χ4622-2-222-2-2-1-2-222-2-2221-1-1-1111-2211-1-1-111-100002i−2i002i−2i0000001-1−33−33−33−33i3i3−i3−i3i3i3−i3−i3000000−ii−ii000000000000
χ4722-2-222-2-2-1-2-222-2-2221-1-1-1111-2211-1-1-111-10000−2i2i00−2i2i0000001-13−33−33−33−3i3i3−i3−i3i3i3−i3−i3000000i−ii−i000000000000
χ4822-2-222-2-2-1-2-222-2-2221-1-1-1111-2211-1-1-111-10000−2i2i00−2i2i0000001-1−33−33−33−33−i3−i3i3i3−i3−i3i3i3000000i−ii−i000000000000
χ4922-2-222-2-2-1-2-2-2-222221-1-1-11112-211-111-1-1-100002i−2i00−2i2i000000-113−33−3−33−33−i3−i3i3i3i3i3−i3−i3000000−iii−i000000000000
χ5022-2-222-2-2-1-2-2-2-222221-1-1-11112-211-111-1-1-100002i−2i00−2i2i000000-11−33−333−33−3i3i3−i3−i3−i3−i3i3i3000000−iii−i000000000000
χ5122-2-222-2-2-1-2-2-2-222221-1-1-11112-211-111-1-1-10000−2i2i002i−2i000000-113−33−3−33−33i3i3−i3−i3−i3−i3i3i3000000i−i−ii000000000000
χ5222-2-222-2-2-1-2-2-2-222221-1-1-11112-211-111-1-1-10000−2i2i002i−2i000000-11−33−333−33−3−i3−i3i3i3i3i3−i3−i3000000i−i−ii000000000000
χ532-22-22-2-222002i−2i2i−2i002-22-2-2-22000002i−2i2i−2i02i−2i2i−2i000000002−2−i2i200000000002−22−2−i2i2−i2i200002-2000000000000−i2i22−2
χ542-22-22-2-222002i−2i2i−2i002-22-2-2-22000002i−2i2i−2i02i−2i2i−2i00000000−22i2−i20000000000−22−22i2−i2i2−i200002-2000000000000i2−i2−22
χ552-22-22-2-222002i−2i2i−2i002-22-2-2-22000002i−2i2i−2i0−2i2i−2i2i000000002−2−i2i200000000002−22−2−i2i2−i2i20000-22000000000000i2−i2−22
χ562-22-22-2-222002i−2i2i−2i002-22-2-2-22000002i−2i2i−2i0−2i2i−2i2i00000000−22i2−i20000000000−22−22i2−i2i2−i20000-22000000000000−i2i22−2
χ572-22-22-2-22200−2i2i−2i2i002-22-2-2-2200000−2i2i−2i2i02i−2i2i−2i000000002−2i2−i200000000002−22−2i2−i2i2−i20000-22000000000000−i2i2−22
χ582-22-22-2-22200−2i2i−2i2i002-22-2-2-2200000−2i2i−2i2i02i−2i2i−2i00000000−22−i2i20000000000−22−22−i2i2−i2i20000-22000000000000i2−i22−2
χ592-22-22-2-22200−2i2i−2i2i002-22-2-2-2200000−2i2i−2i2i0−2i2i−2i2i000000002−2i2−i200000000002−22−2i2−i2i2−i200002-2000000000000i2−i22−2
χ602-22-22-2-22200−2i2i−2i2i002-22-2-2-2200000−2i2i−2i2i0−2i2i−2i2i00000000−22−i2i20000000000−22−22−i2i2−i2i200002-2000000000000−i2i2−22
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-4-44-444-40000-4444-4-4-44-4004-440000-400000000000000000000000000000000000000000000000000000000
χ64444-4-4-44-44-4400004-444-4-4-44-400-44-40000400000000000000000000000000000000000000000000000000000000
χ65444-4-4-44-4-24-40000-44-2-2222-2200-22-200002000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ66444-4-4-44-4-24-40000-44-2-2222-2200-22-2000020000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ67444-4-4-44-4-2-4400004-4-2-2222-22002-220000-2000000000000000000000023−23−2323000000000000000000000000000000
χ68444-4-4-44-4-2-4400004-4-2-2222-22002-220000-20000000000000000000000−232323−23000000000000000000000000000000
χ6944-44-4-4-44-24-400004-42-222-22-200-2220000-200000000004-40000000000-2-222000000000000000000000000000000
χ7044-44-4-4-44-24-400004-42-222-22-200-2220000-20000000000-44000000000022-2-2000000000000000000000000000000
χ7144-44-4-4-44-2-440000-442-222-22-2002-2-2000020000004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000000
χ7244-44-4-4-44-2-440000-442-222-22-2002-2-200002000000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000000
χ7344-4-444-4-4-24444-4-4-4-42-2-2-22224-4-2-22-2-22220000000000000000-2200000000000000000000000000000000000000
χ7444-4-444-4-4-244-4-444-4-42-2-2-2222-44-2-2222-2-2200000000000000002-200000000000000000000000000000000000000
χ754-444-44-4-44000000004-4-444-4-400000000000000000000000000000000000000000000004-4000000000000000000
χ764-444-44-4-44000000004-4-444-4-40000000000000000000000000000000000000000000000-44000000000000000000
χ774-44-44-4-44-2004i−4i4i−4i00-22-2222-200000−2i2i−2i2i000000000000022−22−2i22i20000000000−22−22i2−i2i2−i20000000000000000000000
χ784-44-44-4-44-2004i−4i4i−4i00-22-2222-200000−2i2i−2i2i0000000000000−22222i2−2i200000000002−22−2−i2i2−i2i20000000000000000000000
χ794-44-44-4-44-200−4i4i−4i4i00-22-2222-2000002i−2i2i−2i000000000000022−222i2−2i20000000000−22−22−i2i2−i2i20000000000000000000000
χ804-44-44-4-44-200−4i4i−4i4i00-22-2222-2000002i−2i2i−2i0000000000000−2222−2i22i200000000002−22−2i2−i2i2−i20000000000000000000000
χ814-4-444-44-44004i−4i−4i4i00-4-44-444-4000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000
χ824-4-444-44-4400−4i4i4i−4i00-4-44-444-400000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000
χ834-4-444-44-4-2004i−4i−4i4i0022-22-2-2200000−2i2i2i−2i000000000000000000000000000i6−i6−i6i66−6−660000000000000000000000
χ844-4-444-44-4-2004i−4i−4i4i0022-22-2-2200000−2i2i2i−2i000000000000000000000000000−i6i6i6−i6−666−60000000000000000000000
χ854-4-444-44-4-200−4i4i4i−4i0022-22-2-22000002i−2i−2i2i000000000000000000000000000i6−i6−i6i6−666−60000000000000000000000
χ864-4-444-44-4-200−4i4i4i−4i0022-22-2-22000002i−2i−2i2i000000000000000000000000000−i6i6i6−i66−6−660000000000000000000000
χ874-4-4-4-4444400000000-4-4-44-44400000000004-4-440000000000000000000000000000000000000000000000000000
χ884-4-4-4-4444400000000-4-4-44-4440000000000-444-40000000000000000000000000000000000000000000000000000
χ898-888-88-8-8-400000000-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8-8888-400000000444-44-4-4000000000000000000000000000000000000000000000000000000000000000000

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