Finite Group Databasebeta

← Group #10896465

Character table — Group #10896465

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order122222223444444446666666441212121212121212444444444444888812121212121212121212242424242424242444444412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1
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
χ61111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
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
χ911111111111-1-1-1-1111111111-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111
χ1111111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111
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
χ1311111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1411111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-11111-1-1-1-111-1-1
χ1511111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111111-1-1
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
χ17222222222-2-22222-2-22222222-2-2-2-22222-2-22222000000000000-2-20000000000000000-2-2-2-2220000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-22222-2-2-2-2-2-2000000000000-2-200000000000000002222-2-20000000000000000
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
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-100002222-2-2-2-222-2-211-1-1-1-11111-1-1-1-11111000000-1-111000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-1000022-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-100000011-1-1000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-2-2-2222222-2-2111111-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ2922-22-2-22-22220000-2-22-22-22-2-200220000-2-222-2-2002-2000000000022-2-20000000000002-200000000002-200000000
χ3022-22-2-22-22220000-2-22-22-22-2-200220000-2-222-2-200-220000000000-2-2220000000000002-20000000000-2200000000
χ3122-22-2-22-22220000-2-22-22-22-2-200220000-2-2-2-222002-2000000000022-2-2000000000000-220000000000-2200000000
χ3222-22-2-22-22220000-2-22-22-22-2-200220000-2-2-2-22200-220000000000-2-222000000000000-2200000000002-200000000
χ3322-22-2-22-22-2-20000222-22-22-2-200-2-200002222-2-20000002i−2i00000000002i2i−2i−2i00000000-22000000000000002i−2i0000
χ3422-22-2-22-22-2-20000222-22-22-2-200-2-200002222-2-2000000−2i2i0000000000−2i−2i2i2i00000000-2200000000000000−2i2i0000
χ3522-22-2-22-22-2-20000222-22-22-2-200-2-2000022-2-2220000002i−2i00000000002i2i−2i−2i000000002-200000000000000−2i2i0000
χ3622-22-2-22-22-2-20000222-22-22-2-200-2-2000022-2-222000000−2i2i0000000000−2i−2i2i2i000000002-2000000000000002i−2i0000
χ3722-2-22-2-2222-22i2i−2i−2i2-2-222-2-2-222i−2i2-22i2i−2i−2i2-200000000000000002i−2i000000000000000000000000002i−2i002-2000000
χ3822-2-22-2-2222-22i2i−2i−2i2-2-222-2-2-222i−2i2-22i2i−2i−2i2-200000000000000002i−2i00000000000000000000000000−2i2i00-22000000
χ3922-2-22-2-2222-2−2i−2i2i2i2-2-222-2-2-22−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i000000000000000000000000002i−2i00-22000000
χ4022-2-22-2-2222-2−2i−2i2i2i2-2-222-2-2-22−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i00000000000000000000000000−2i2i002-2000000
χ4122-2-22-2-222-222i2i−2i−2i-22-222-2-2-22−2i2i-222i2i−2i−2i-2200002i−2i002-2000000−2i2i00000000000000000000002i−2i2-2000000000000
χ4222-2-22-2-222-222i2i−2i−2i-22-222-2-2-22−2i2i-222i2i−2i−2i-220000−2i2i00-22000000−2i2i0000000000000000000000−2i2i-22000000000000
χ4322-2-22-2-222-22−2i−2i2i2i-22-222-2-2-222i−2i-22−2i−2i2i2i-2200002i−2i00-220000002i−2i00000000000000000000002i−2i-22000000000000
χ4422-2-22-2-222-22−2i−2i2i2i-22-222-2-2-222i−2i-22−2i−2i2i2i-220000−2i2i002-20000002i−2i0000000000000000000000−2i2i2-2000000000000
χ4522-2-22-2-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-100002i−2i002-2000000i−i3−33−3−i3i3−i3i3−i3−i3i3i333−3−3000000−ii-11000000000000
χ4622-2-22-2-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-100002i−2i002-2000000i−i−33−33i3−i3i3−i3i3i3−i3−i3−3−333000000−ii-11000000000000
χ4722-2-22-2-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-10000−2i2i00-22000000i−i3−33−3−i3i3−i3i3i3i3−i3−i3−3−333000000i−i1-1000000000000
χ4822-2-22-2-22-1-222i2i−2i−2i-221-1-1111-1−2i2i1-1−i−iii1-10000−2i2i00-22000000i−i−33−33i3−i3i3−i3−i3−i3i3i333−3−3000000i−i1-1000000000000
χ4922-2-22-2-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-100002i−2i00-22000000−ii3−33−3i3−i3i3−i3−i3−i3i3i3−3−333000000−ii1-1000000000000
χ5022-2-22-2-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-100002i−2i00-22000000−ii−33−33−i3i3−i3i3i3i3−i3−i333−3−3000000−ii1-1000000000000
χ5122-2-22-2-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-10000−2i2i002-2000000−ii3−33−3i3−i3i3−i3i3i3−i3−i333−3−3000000i−i-11000000000000
χ5222-2-22-2-22-1-22−2i−2i2i2i-221-1-1111-12i−2i1-1ii−i−i1-10000−2i2i002-2000000−ii−33−33−i3i3−i3i3−i3−i3i3i3−3−333000000i−i-11000000000000
χ532-2-2-2-22222002-22-200-2-2-2-222200002-22-2002-22-2000000002−22−200000000002−22−22−22−200002-20000000000002−22−2
χ542-2-2-2-22222002-22-200-2-2-2-222200002-22-2002-22-200000000−22−220000000000−22−22−22−2200002-2000000000000−22−22
χ552-2-2-2-22222002-22-200-2-2-2-222200002-22-200-22-22000000002−22−200000000002−22−22−22−20000-22000000000000−22−22
χ562-2-2-2-22222002-22-200-2-2-2-222200002-22-200-22-2200000000−22−220000000000−22−22−22−220000-220000000000002−22−2
χ572-2-2-2-2222200-22-2200-2-2-2-22220000-22-22002-22-2000000002−2−2200000000002−22−2−22−220000-220000000000002−2−22
χ582-2-2-2-2222200-22-2200-2-2-2-22220000-22-22002-22-200000000−222−20000000000−22−222−22−20000-22000000000000−222−2
χ592-2-2-2-2222200-22-2200-2-2-2-22220000-22-2200-22-22000000002−2−2200000000002−22−2−22−2200002-2000000000000−222−2
χ602-2-2-2-2222200-22-2200-2-2-2-22220000-22-2200-22-2200000000−222−20000000000−22−222−22−200002-20000000000002−2−22
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-44-4-444-40000-44-4-444-44-4004-40000-4400000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-44-4400004-4-4-444-44-400-4400004-400000000000000000000000000000000000000000000000000000000
χ65444-4-44-4-4-24-40000-4422-2-22-2200-2200002-2000000000000000000000023−23−2323000000000000000000000000000000
χ66444-4-44-4-4-24-40000-4422-2-22-2200-2200002-20000000000000000000000−232323−23000000000000000000000000000000
χ67444-4-44-4-4-2-4400004-422-2-22-22002-20000-2200000000000000000023−23−23230000000000000000000000000000000000
χ68444-4-44-4-4-2-4400004-422-2-22-22002-20000-22000000000000000000−232323−230000000000000000000000000000000000
χ6944-44-4-44-4-2440000-4-4-22-22-22200-2-20000220000004-40000000000-2-2220000000000000000000000000000000000
χ7044-44-4-44-4-2440000-4-4-22-22-22200-2-2000022000000-44000000000022-2-20000000000000000000000000000000000
χ7144-44-4-44-4-2-4-4000044-22-22-22200220000-2-200000000004i−4i0000000000−2i−2i2i2i000000000000000000000000000000
χ7244-44-4-44-4-2-4-4000044-22-22-22200220000-2-20000000000−4i4i00000000002i2i−2i−2i000000000000000000000000000000
χ7344-4-44-4-44-24-44i4i−4i−4i4-42-2-2222-24i−4i-22−2i−2i2i2i-220000000000000000−2i2i00000000000000000000000000000000000000
χ7444-4-44-4-44-24-4−4i−4i4i4i4-42-2-2222-2−4i4i-222i2i−2i−2i-2200000000000000002i−2i00000000000000000000000000000000000000
χ754-444-4-4-444004i−4i−4i4i004-4-44-4-4400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ764-444-4-4-44400−4i4i4i−4i004-4-44-4-440000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ774-444-4-4-44-2004i−4i−4i4i00-222-222-20000−2i2i2i−2i0000000000000000000000000000i6−i6−i6i6−666−60000000000000000000000
χ784-444-4-4-44-2004i−4i−4i4i00-222-222-20000−2i2i2i−2i0000000000000000000000000000−i6i6i6−i66−6−660000000000000000000000
χ794-444-4-4-44-200−4i4i4i−4i00-222-222-200002i−2i−2i2i0000000000000000000000000000i6−i6−i6i66−6−660000000000000000000000
χ804-444-4-4-44-200−4i4i4i−4i00-222-222-200002i−2i−2i2i0000000000000000000000000000−i6i6i6−i6−666−60000000000000000000000
χ814-44-44-44-4400000000-44-444-4-400000000004-4-440000000000000000000000000000000000000000000000000000
χ824-44-44-44-4400000000-44-444-4-40000000000-444-40000000000000000000000000000000000000000000000000000
χ834-4-4444-4-440000000044-4-4-44-400000000000000000000000000000000000000000000004-4000000000000000000
χ844-4-4444-4-440000000044-4-4-44-40000000000000000000000000000000000000000000000-44000000000000000000
χ854-4-4-4-4444-2004-44-4002222-2-2-20000-22-220000000000000022−2222−220000000000−22−22−22−220000000000000000000000
χ864-4-4-4-4444-2004-44-4002222-2-2-20000-22-2200000000000000−2222−222200000000002−22−22−22−20000000000000000000000
χ874-4-4-4-4444-200-44-44002222-2-2-200002-22-20000000000000022−22−22220000000000−22−222−22−20000000000000000000000
χ884-4-4-4-4444-200-44-44002222-2-2-200002-22-200000000000000−222222−2200000000002−22−2−22−220000000000000000000000
χ898-88-88-88-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000

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