Finite Group Databasebeta

← Group #10896483

Character table — Group #10896483

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order122222223444444446666666441212121212121212444444444444888812121212121212121212242424242424242444444412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
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
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-1111111111-1-111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111
χ1111111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1211111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1311111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1411111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-111-1-111-1-111-1-1
χ1511111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-11111-1-1
χ1611111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111
χ17222222222-2-22222-2-22222222-2-2-2-22222-2-222220000000000000000-2-2000000000000-2-2-2-2220000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2-20000000000002222-2-20000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22222000000000000000022000000000000-2-222-2-20000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002200000000000022-2-2220000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022-2-222-2-2-2-2-2-21111-1-1111111111111000000-1-1-1-1000000000000
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
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-10000001111000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-100002222-2-2-2-222-2-2-1-1-1-1111111-1-1-1-11111000000-1-111000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-1000022-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-22222-2-2-2-222-1-1-1-11111111111-1-1-1-100000011-1-1000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-2-2-2222222-2-2111111-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ29222-2-2-22-22220000-2-22-22-22-2-200220000-2-222-2-2002-20000000022-2-2000000000000002-20000000000002-2000000
χ30222-2-2-22-22220000-2-22-22-22-2-200220000-2-222-2-200-2200000000-2-222000000000000002-2000000000000-22000000
χ31222-2-2-22-22220000-2-22-22-22-2-200220000-2-2-2-222002-20000000022-2-200000000000000-22000000000000-22000000
χ32222-2-2-22-22220000-2-22-22-22-2-200220000-2-2-2-22200-2200000000-2-22200000000000000-220000000000002-2000000
χ33222-2-2-22-22-2-20000222-22-22-2-200-2-200002222-2-20000002i−2i00000000002i2i−2i−2i00000000-22000000000000002i−2i0000
χ34222-2-2-22-22-2-20000222-22-22-2-200-2-200002222-2-2000000−2i2i0000000000−2i−2i2i2i00000000-2200000000000000−2i2i0000
χ35222-2-2-22-22-2-20000222-22-22-2-200-2-2000022-2-2220000002i−2i00000000002i2i−2i−2i000000002-200000000000000−2i2i0000
χ36222-2-2-22-22-2-20000222-22-22-2-200-2-2000022-2-222000000−2i2i0000000000−2i−2i2i2i000000002-2000000000000002i−2i0000
χ3722-2-2-22-2222-22i2i−2i−2i2-2-222-2-2-222i−2i2-22i2i−2i−2i2-2000000000000000000002i−2i00000000000000000000002i−2i2-200000000
χ3822-2-2-22-2222-22i2i−2i−2i2-2-222-2-2-222i−2i2-22i2i−2i−2i2-2000000000000000000002i−2i0000000000000000000000−2i2i-2200000000
χ3922-2-2-22-2222-2−2i−2i2i2i2-2-222-2-2-22−2i2i2-2−2i−2i2i2i2-200000000000000000000−2i2i00000000000000000000002i−2i-2200000000
χ4022-2-2-22-2222-2−2i−2i2i2i2-2-222-2-2-22−2i2i2-2−2i−2i2i2i2-200000000000000000000−2i2i0000000000000000000000−2i2i2-200000000
χ4122-2-2-22-222-222i2i−2i−2i-22-222-2-2-22−2i2i-222i2i−2i−2i-2200002i−2i002-20000000000−2i2i0000000000000000002i−2i2-2000000000000
χ4222-2-2-22-222-222i2i−2i−2i-22-222-2-2-22−2i2i-222i2i−2i−2i-220000−2i2i00-220000000000−2i2i000000000000000000−2i2i-22000000000000
χ4322-2-2-22-222-22−2i−2i2i2i-22-222-2-2-222i−2i-22−2i−2i2i2i-2200002i−2i00-2200000000002i−2i0000000000000000002i−2i-22000000000000
χ4422-2-2-22-222-22−2i−2i2i2i-22-222-2-2-222i−2i-22−2i−2i2i2i-220000−2i2i002-200000000002i−2i000000000000000000−2i2i2-2000000000000
χ4522-2-2-22-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-100002i−2i002-20000003−33−3i−i−i3i3−i3i3−i3−i3i3i333−3−3000000−ii-11000000000000
χ4622-2-2-22-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-100002i−2i002-2000000−33−33i−ii3−i3i3−i3i3i3−i3−i3−3−333000000−ii-11000000000000
χ4722-2-2-22-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-10000−2i2i00-220000003−33−3i−i−i3i3−i3i3i3i3−i3−i3−3−333000000i−i1-1000000000000
χ4822-2-2-22-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-10000−2i2i00-22000000−33−33i−ii3−i3i3−i3−i3−i3i3i333−3−3000000i−i1-1000000000000
χ4922-2-2-22-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-100002i−2i00-220000003−33−3−iii3−i3i3−i3−i3−i3i3i3−3−333000000−ii1-1000000000000
χ5022-2-2-22-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-100002i−2i00-22000000−33−33−ii−i3i3−i3i3i3i3−i3−i333−3−3000000−ii1-1000000000000
χ5122-2-2-22-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-10000−2i2i002-20000003−33−3−iii3−i3i3−i3i3i3−i3−i333−3−3000000i−i-11000000000000
χ5222-2-2-22-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-10000−2i2i002-2000000−33−33−ii−i3i3−i3i3−i3−i3i3i3−3−333000000i−i-11000000000000
χ532-2-22-222-22002i−2i2i−2i00-22-2-222-200002i−2i2i−2i002-22-2000000002−2−i2i200000000002−22−2−i2i2−i2i200002i−2i0000000000002−2−i2i2
χ542-2-22-222-22002i−2i2i−2i00-22-2-222-200002i−2i2i−2i002-22-200000000−22i2−i20000000000−22−22i2−i2i2−i200002i−2i000000000000−22i2−i2
χ552-2-22-222-22002i−2i2i−2i00-22-2-222-200002i−2i2i−2i00-22-22000000002−2−i2i200000000002−22−2−i2i2−i2i20000−2i2i000000000000−22i2−i2
χ562-2-22-222-22002i−2i2i−2i00-22-2-222-200002i−2i2i−2i00-22-2200000000−22i2−i20000000000−22−22i2−i2i2−i20000−2i2i0000000000002−2−i2i2
χ572-2-22-222-2200−2i2i−2i2i00-22-2-222-20000−2i2i−2i2i002-22-2000000002−2i2−i200000000002−22−2i2−i2i2−i20000−2i2i0000000000002−2i2−i2
χ582-2-22-222-2200−2i2i−2i2i00-22-2-222-20000−2i2i−2i2i002-22-200000000−22−i2i20000000000−22−22−i2i2−i2i20000−2i2i000000000000−22−i2i2
χ592-2-22-222-2200−2i2i−2i2i00-22-2-222-20000−2i2i−2i2i00-22-22000000002−2i2−i200000000002−22−2i2−i2i2−i200002i−2i000000000000−22−i2i2
χ602-2-22-222-2200−2i2i−2i2i00-22-2-222-20000−2i2i−2i2i00-22-2200000000−22−i2i20000000000−22−22−i2i2−i2i200002i−2i0000000000002−2i2−i2
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000000000000220000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000000000000000-2-20000000000000000000000000000000000
χ63444-4-4-44-4-2440000-4-4-22-22-22200-2-20000220000004-400000000-2-222000000000000000000000000000000000000
χ64444-4-4-44-4-2440000-4-4-22-22-22200-2-2000022000000-440000000022-2-2000000000000000000000000000000000000
χ65444-4-4-44-4-2-4-4000044-22-22-22200220000-2-200000000004i−4i0000000000−2i−2i2i2i000000000000000000000000000000
χ66444-4-4-44-4-2-4-4000044-22-22-22200220000-2-20000000000−4i4i00000000002i2i−2i−2i000000000000000000000000000000
χ6744-444-4-4-444-40000-44-4-444-44-4004-40000-4400000000000000000000000000000000000000000000000000000000
χ6844-444-4-4-44-4400004-4-4-444-44-400-4400004-400000000000000000000000000000000000000000000000000000000
χ6944-444-4-4-4-24-40000-4422-2-22-2200-2200002-2000000000000000000000023−23−2323000000000000000000000000000000
χ7044-444-4-4-4-24-40000-4422-2-22-2200-2200002-20000000000000000000000−232323−23000000000000000000000000000000
χ7144-444-4-4-4-2-4400004-422-2-22-22002-20000-22000000000000000023−23−2323000000000000000000000000000000000000
χ7244-444-4-4-4-2-4400004-422-2-22-22002-20000-220000000000000000−232323−23000000000000000000000000000000000000
χ7344-4-4-44-44-24-44i4i−4i−4i4-42-2-2222-24i−4i-22−2i−2i2i2i-2200000000000000000000−2i2i0000000000000000000000000000000000
χ7444-4-4-44-44-24-4−4i−4i4i4i4-42-2-2222-2−4i4i-222i2i−2i−2i-22000000000000000000002i−2i0000000000000000000000000000000000
χ754-444-4-4-444000000004-4-4-4-44400000000000000000000000000000000000000000000004i−4i000000000000000000
χ764-444-4-4-444000000004-4-4-4-4440000000000000000000000000000000000000000000000−4i4i000000000000000000
χ774-44-444-4-44004-4-440044-44-4-4-400004-4-440000000000000000000000000000000000000000000000000000000000
χ784-44-444-4-4400-444-40044-44-4-4-40000-444-40000000000000000000000000000000000000000000000000000000000
χ794-44-444-4-4-2004-4-4400-2-22-22220000-222-20000000000000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ804-44-444-4-4-2004-4-4400-2-22-22220000-222-20000000000000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ814-44-444-4-4-200-444-400-2-22-222200002-2-220000000000000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ824-44-444-4-4-200-444-400-2-22-222200002-2-220000000000000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ834-4-44-444-4-2004i−4i4i−4i002-222-2-220000−2i2i−2i2i0000000000000022−22−2i22i20000000000−22−22i2−i2i2−i20000000000000000000000
χ844-4-44-444-4-2004i−4i4i−4i002-222-2-220000−2i2i−2i2i00000000000000−22222i2−2i200000000002−22−2−i2i2−i2i20000000000000000000000
χ854-4-44-444-4-200−4i4i−4i4i002-222-2-2200002i−2i2i−2i0000000000000022−222i2−2i20000000000−22−22−i2i2−i2i20000000000000000000000
χ864-4-44-444-4-200−4i4i−4i4i002-222-2-2200002i−2i2i−2i00000000000000−2222−2i22i200000000002−22−2i2−i2i2−i20000000000000000000000
χ874-4-4-44-444400000000-4-4-444-4400000000004-4-440000000000000000000000000000000000000000000000000000
χ884-4-4-44-444400000000-4-4-444-440000000000-444-40000000000000000000000000000000000000000000000000000
χ898-888-8-8-88-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-88-888-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000

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