Finite Group Databasebeta

← Group #10876128

Character table — Group #10876128

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order122222223444444446666666441212121212121212222244444444888812121212121212121212242424242424242444444412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
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
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
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
χ9111111111-1-1-1-111111111111-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-111111111111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111
χ11111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ12111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-22222000000000000-2-2000000000000000022-2-2-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2000000000000-2-20000000000000000-2-222220000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000001111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-22222-2-2-2-2-1-11111111111111111000000-1-1-1-1000000000000
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
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-222-2-222-2-211-1-1-1-11111-1-1-1-11111000000-1-111000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-100000011-1-1000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ2922-2-22-2-2222i2i−2i−2i2-22-22-2-22-2-222i−2i2i2i−2i−2i2-22-200000000000000002i−2i0000000000000000000000000000002i−2i2-20000
χ3022-2-22-2-2222i2i−2i−2i2-22-22-2-22-2-222i−2i2i2i−2i−2i2-22-200000000000000002i−2i000000000000000000000000000000−2i2i-220000
χ3122-2-22-2-2222i2i−2i−2i-22-222-2-22-2-22−2i2i2i2i−2i−2i-22-22000000002i−2i2-20000−2i2i00000000000000000000002i−2i2-2000000000000
χ3222-2-22-2-2222i2i−2i−2i-22-222-2-22-2-22−2i2i2i2i−2i−2i-22-2200000000−2i2i-220000−2i2i0000000000000000000000−2i2i-22000000000000
χ3322-2-22-2-222−2i−2i2i2i2-22-22-2-22-2-22−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i0000000000000000000000000000002i−2i-220000
χ3422-2-22-2-222−2i−2i2i2i2-22-22-2-22-2-22−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i000000000000000000000000000000−2i2i2-20000
χ3522-2-22-2-222−2i−2i2i2i-22-222-2-22-2-222i−2i−2i−2i2i2i-22-22000000002i−2i-2200002i−2i00000000000000000000002i−2i-22000000000000
χ3622-2-22-2-222−2i−2i2i2i-22-222-2-22-2-222i−2i−2i−2i2i2i-22-2200000000−2i2i2-200002i−2i0000000000000000000000−2i2i2-2000000000000
χ3722-2-22-2-22-12i2i−2i−2i-22-22-111-111-1−2i2i−i−iii1-11-1000000002i−2i2-20000i−i−i3−i3i3i333−3−333−3−3−i3−i3i3i3000000−ii-11000000000000
χ3822-2-22-2-22-12i2i−2i−2i-22-22-111-111-1−2i2i−i−iii1-11-1000000002i−2i2-20000i−ii3i3−i3−i3−3−333−3−333i3i3−i3−i3000000−ii-11000000000000
χ3922-2-22-2-22-12i2i−2i−2i-22-22-111-111-1−2i2i−i−iii1-11-100000000−2i2i-220000i−i−i3−i3i3i333−3−3−3−333i3i3−i3−i3000000i−i1-1000000000000
χ4022-2-22-2-22-12i2i−2i−2i-22-22-111-111-1−2i2i−i−iii1-11-100000000−2i2i-220000i−ii3i3−i3−i3−3−33333−3−3−i3−i3i3i3000000i−i1-1000000000000
χ4122-2-22-2-22-1−2i−2i2i2i-22-22-111-111-12i−2iii−i−i1-11-1000000002i−2i-220000−ii−i3−i3i3i3−3−33333−3−3i3i3−i3−i3000000−ii1-1000000000000
χ4222-2-22-2-22-1−2i−2i2i2i-22-22-111-111-12i−2iii−i−i1-11-1000000002i−2i-220000−iii3i3−i3−i333−3−3−3−333−i3−i3i3i3000000−ii1-1000000000000
χ4322-2-22-2-22-1−2i−2i2i2i-22-22-111-111-12i−2iii−i−i1-11-100000000−2i2i2-20000−ii−i3−i3i3i3−3−333−3−333−i3−i3i3i3000000i−i-11000000000000
χ4422-2-22-2-22-1−2i−2i2i2i-22-22-111-111-12i−2iii−i−i1-11-100000000−2i2i2-20000−iii3i3−i3−i333−3−333−3−3i3i3−i3−i3000000i−i-11000000000000
χ452-222-2-2-22200002-2-22-222-2-2-22000000-222-222-2-22i−2i0000000000002i−2i2i−2i00000000000000002-200002i−2i0000000000
χ462-222-2-2-22200002-2-22-222-2-2-22000000-222-222-2-2−2i2i000000000000−2i2i−2i2i00000000000000002-20000−2i2i0000000000
χ472-222-2-2-22200002-2-22-222-2-2-22000000-222-2-2-2222i−2i0000000000002i−2i2i−2i0000000000000000-220000−2i2i0000000000
χ482-222-2-2-22200002-2-22-222-2-2-22000000-222-2-2-222−2i2i000000000000−2i2i−2i2i0000000000000000-2200002i−2i0000000000
χ492-222-2-2-2220000-222-2-222-2-2-220000002-2-2222-2-2002i−2i000000000000002i−2i2i−2i000000000000-220000002i−2i00000000
χ502-222-2-2-2220000-222-2-222-2-2-220000002-2-2222-2-200−2i2i00000000000000−2i2i−2i2i000000000000-22000000−2i2i00000000
χ512-222-2-2-2220000-222-2-222-2-2-220000002-2-22-2-222002i−2i000000000000002i−2i2i−2i0000000000002-2000000−2i2i00000000
χ522-222-2-2-2220000-222-2-222-2-2-220000002-2-22-2-22200−2i2i00000000000000−2i2i−2i2i0000000000002-20000002i−2i00000000
χ532-22-222-2-222-22-20000-22-222-2-2002-22-200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22-20000000000000000−i2i2−i2i2
χ542-22-222-2-222-22-20000-22-222-2-2002-22-200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22-20000000000000000i2−i2i2−i2
χ552-22-222-2-222-22-20000-22-222-2-2002-22-20000-22-2200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2-220000000000000000i2−i2i2−i2
χ562-22-222-2-222-22-20000-22-222-2-2002-22-20000-22-2200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2-220000000000000000−i2i2−i2i2
χ572-22-222-2-22-22-220000-22-222-2-200-22-2200002-22-200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2-220000000000000000−i2i2i2−i2
χ582-22-222-2-22-22-220000-22-222-2-200-22-2200002-22-200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2-220000000000000000i2−i2−i2i2
χ592-22-222-2-22-22-220000-22-222-2-200-22-220000-22-2200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22-20000000000000000i2−i2−i2i2
χ602-22-222-2-22-22-220000-22-222-2-200-22-220000-22-2200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22-20000000000000000−i2i2i2−i2
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-4-44-440000000044-4-4-44-400000000004-4-440000000000000000000000000000000000000000000000000000
χ64444-4-4-44-440000000044-4-4-44-40000000000-444-40000000000000000000000000000000000000000000000000000
χ6544-44-44-4-44000000004-44-44-4-400000000000000000000000000000000000000000000004-4000000000000000000
χ6644-44-44-4-44000000004-44-44-4-40000000000000000000000000000000000000000000000-44000000000000000000
χ6744-4-44-4-44-24i4i−4i−4i4-44-4-222-222-24i−4i−2i−2i2i2i-22-220000000000000000−2i2i00000000000000000000000000000000000000
χ6844-4-44-4-44-2−4i−4i4i4i4-44-4-222-222-2−4i4i2i2i−2i−2i-22-2200000000000000002i−2i00000000000000000000000000000000000000
χ694-444-4-4-44-200004-4-442-2-2222-20000002-2-2200004i−4i000000000000−2i2i−2i2i0000000000000000000000000000000000
χ704-444-4-4-44-200004-4-442-2-2222-20000002-2-220000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000000
χ714-444-4-4-44-20000-444-42-2-2222-2000000-222-20000004i−4i00000000000000−2i2i−2i2i000000000000000000000000000000
χ724-444-4-4-44-20000-444-42-2-2222-2000000-222-2000000−4i4i000000000000002i−2i2i−2i000000000000000000000000000000
χ734-44-444-4-4-24-44-400002-22-2-22200-22-220000000000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ744-44-444-4-4-24-44-400002-22-2-22200-22-2200000000000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ754-44-444-4-4-2-44-4400002-22-2-222002-22-20000000000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ764-44-444-4-4-2-44-4400002-22-2-222002-22-200000000000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ774-4-444-44-444i−4i−4i4i0000-4-444-44-4004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ784-4-444-44-44−4i4i4i−4i0000-4-444-44-400−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ794-4-444-44-4-24i−4i−4i4i000022-2-22-2200−2i2i2i−2i000000000000000000000000000000i6−i6−i6i66−6−660000000000000000000000
χ804-4-444-44-4-24i−4i−4i4i000022-2-22-2200−2i2i2i−2i000000000000000000000000000000−i6i6i6−i6−666−60000000000000000000000
χ814-4-444-44-4-2−4i4i4i−4i000022-2-22-22002i−2i−2i2i000000000000000000000000000000i6−i6−i6i6−666−60000000000000000000000
χ824-4-444-44-4-2−4i4i4i−4i000022-2-22-22002i−2i−2i2i000000000000000000000000000000−i6i6i6−i66−6−660000000000000000000000
χ834-4-4-4-44444000044-4-4-4-4-4-4444000000-4-44400000000000000000000000000000000000000000000000000000000
χ844-4-4-4-444440000-4-444-4-4-4-444400000044-4-400000000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-2000044-4-42222-2-2-200000022-2-20000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ864-4-4-4-4444-2000044-4-42222-2-2-200000022-2-200000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ874-4-4-4-4444-20000-4-4442222-2-2-2000000-2-22200000000000000000023−23−23230000000000000000000000000000000000
χ884-4-4-4-4444-20000-4-4442222-2-2-2000000-2-222000000000000000000−232323−230000000000000000000000000000000000
χ89888-8-8-88-8-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-88-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000

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