Finite Group Databasebeta

← Group #10867966

Character table — Group #10867966

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order12222222344444444666666644444412121212121212122266668888121212121212242424242424242444448888888844121212122444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-111-1-1
χ9111111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-1-1111-1-111
χ10111111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-11-1-111111-1-1-111-1-1
χ11111111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-111111-1-1-1-1
χ12111111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-1-11-111-1-11-1-1-1-1-11111
χ13111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1-111-1-1111-1-1
χ14111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-11-1-111-1-1-111
χ15111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-1-1-1-111111
χ16111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11-1-11111111-1-1-1-1-1
χ172222222222222-2-2-2-222222220000-2-2-2-22222-2-20000000000-2-2000000000000222200000000000000-20000-20000
χ182222222222222-2-2-2-222222220000-2-2-2-22222-2-20000000000-2-2000000000000-2-2-2-2000000000000002000020000
χ19222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-200000000002200000000000022-2-20000000000000020000-20000
χ20222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-2000000000022000000000000-2-22200000000000000-2000020000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-111111111111100000000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2111122-2-211-1-1-1-1-1-1-1-11111000000000000-2211-1-10000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-21111-2-22211-1-1-1-11111-1-1-1-10000000000002-2-1-1110000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-1-1-1-122-2-2111111-1-1-1-111110000000000002-2-1-1110000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-1-1-1-1-2-2221111111111-1-1-1-1000000000000-2211-1-10000000000
χ2922-22-2-22-22000022-2-2-2-2-22-22222-2-2002-200002-200000000000022-2-20000000000002i2i−2i−2i0000000000000000002i−2i
χ3022-22-2-22-22000022-2-2-2-2-22-22222-2-2002-200002-200000000000022-2-2000000000000−2i−2i2i2i000000000000000000−2i2i
χ3122-22-2-22-22000022-2-2-2-2-22-222-2-222002-200002-2000000000000-2-2220000000000002i2i−2i−2i000000000000000000−2i2i
χ3222-22-2-22-22000022-2-2-2-2-22-222-2-222002-200002-2000000000000-2-222000000000000−2i−2i2i2i0000000000000000002i−2i
χ3322-2-22-2-22222-2-2000022-2-2-22-20000000022-2-200000000−i2i2−i2i2000000−i2−i2i2i2−i2−i2i2i22i−2i2i−2i2−22−222−2−20000000000000000
χ3422-2-22-2-22222-2-2000022-2-2-22-20000000022-2-200000000−i2i2−i2i2000000−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i−22−22−2−2220000000000000000
χ3522-2-22-2-22222-2-2000022-2-2-22-20000000022-2-200000000i2−i2i2−i2000000i2i2−i2−i2i2i2−i2−i22i−2i2i−2i−22−22−2−2220000000000000000
χ3622-2-22-2-22222-2-2000022-2-2-22-20000000022-2-200000000i2−i2i2−i2000000i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i2−22−222−2−20000000000000000
χ3722-2-22-2-222-2-222000022-2-2-22-200000000-2-22200000000−i2i2i2−i2000000−i2−i2i2i2i2i2−i2−i22i−2i−2i2i2−22−2−2−2220000000000000000
χ3822-2-22-2-222-2-222000022-2-2-22-200000000-2-22200000000−i2i2i2−i2000000−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i−22−2222−2−20000000000000000
χ3922-2-22-2-222-2-222000022-2-2-22-200000000-2-22200000000i2−i2−i2i2000000i2i2−i2−i2−i2−i2i2i22i−2i−2i2i−22−2222−2−20000000000000000
χ4022-2-22-2-222-2-222000022-2-2-22-200000000-2-22200000000i2−i2−i2i2000000i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i2−22−2−2−2220000000000000000
χ412-222-2-2-2220000-22-222-222-2-2-22i−2i2i−2i00-2-20000220000000000002i−2i2i−2i00000000000000002-22-200000002i−2i0000000
χ422-222-2-2-2220000-22-222-222-2-2-22i−2i2i−2i00-2-20000220000000000002i−2i2i−2i0000000000000000-22-220000000−2i2i0000000
χ432-222-2-2-2220000-22-222-222-2-2-2−2i2i−2i2i00-2-2000022000000000000−2i2i−2i2i00000000000000002-22-20000000−2i2i0000000
χ442-222-2-2-2220000-22-222-222-2-2-2−2i2i−2i2i00-2-2000022000000000000−2i2i−2i2i0000000000000000-22-2200000002i−2i0000000
χ452-2-2222-2-222i−2i2i−2i2-2-22-22-222-2-200002i−2i2-22i−2i2i−2i-2200000000002i−2i0000000000000000000000000000000002-202i−2i00
χ462-2-2222-2-222i−2i2i−2i2-2-22-22-222-2-200002i−2i2-22i−2i2i−2i-2200000000002i−2i000000000000000000000000000000000-220−2i2i00
χ472-2-2222-2-222i−2i2i−2i-222-2-22-222-2-22i−2i−2i2i−2i2i-222i−2i2i−2i2-22-222-2-20000−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ482-2-2222-2-222i−2i2i−2i-222-2-22-222-2-2−2i2i2i−2i−2i2i-222i−2i2i−2i2-2-22-2-2220000−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ492-2-2222-2-22−2i2i−2i2i2-2-22-22-222-2-20000−2i2i2-2−2i2i−2i2i-220000000000−2i2i0000000000000000000000000000000002-20−2i2i00
χ502-2-2222-2-22−2i2i−2i2i2-2-22-22-222-2-20000−2i2i2-2−2i2i−2i2i-220000000000−2i2i000000000000000000000000000000000-2202i−2i00
χ512-2-2222-2-22−2i2i−2i2i-222-2-22-222-2-22i−2i−2i2i2i−2i-22−2i2i−2i2i2-2-22-2-22200002i−2i2i−2i−2i2i000000000000000000000000000000000000
χ522-2-2222-2-22−2i2i−2i2i-222-2-22-222-2-2−2i2i2i−2i2i−2i-22−2i2i−2i2i2-22-222-2-200002i−2i−2i2i2i−2i000000000000000000000000000000000000
χ532-2-2222-2-2-12i−2i2i−2i-222-21-11-1-1112i−2i−2i2i−2i2i1-1−ii−ii-112-2-1-1110000i−i−iii−i−i3i3−i3i33−33−300000000000000−i3i33−30000000000
χ542-2-2222-2-2-12i−2i2i−2i-222-21-11-1-1112i−2i−2i2i−2i2i1-1−ii−ii-112-2-1-1110000i−i−iii−ii3−i3i3−i3−33−3300000000000000i3−i3−330000000000
χ552-2-2222-2-2-12i−2i2i−2i-222-21-11-1-111−2i2i2i−2i−2i2i1-1−ii−ii-11-2211-1-10000i−ii−i−ii−i3i3−i3i33−33−300000000000000i3−i3−330000000000
χ562-2-2222-2-2-12i−2i2i−2i-222-21-11-1-111−2i2i2i−2i−2i2i1-1−ii−ii-11-2211-1-10000i−ii−i−iii3−i3i3−i3−33−3300000000000000−i3i33−30000000000
χ572-2-2222-2-2-1−2i2i−2i2i-222-21-11-1-1112i−2i−2i2i2i−2i1-1i−ii−i-11-2211-1-10000−ii−iii−i−i3i3−i3i3−33−3300000000000000i3−i33−30000000000
χ582-2-2222-2-2-1−2i2i−2i2i-222-21-11-1-1112i−2i−2i2i2i−2i1-1i−ii−i-11-2211-1-10000−ii−iii−ii3−i3i3−i33−33−300000000000000−i3i3−330000000000
χ592-2-2222-2-2-1−2i2i−2i2i-222-21-11-1-111−2i2i2i−2i2i−2i1-1i−ii−i-112-2-1-1110000−iii−i−ii−i3i3−i3i3−33−3300000000000000−i3i3−330000000000
χ602-2-2222-2-2-1−2i2i−2i2i-222-21-11-1-111−2i2i2i−2i2i−2i1-1i−ii−i-112-2-1-1110000−iii−i−iii3−i3i3−i33−33−300000000000000i3−i33−30000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-20000-4-422-2-2-2-2220000000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2000044222222220000000000-2-20000000000000000000000000000000000000000
χ63444-4-44-4-4400000000-4-44-444-4000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ64444-4-44-4-4400000000-4-44-444-40000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6544-44-4-44-440000-4-444-4-4-44-444000000-440000-440000000000000000000000000000000000000000000000000000
χ6644-44-4-44-4-2000044-4-4222-22-2-244-4-400-220000-22000000000000-2-222000000000000000000000000000000000000
χ6744-44-4-44-4-2000044-4-4222-22-2-2-4-44400-220000-2200000000000022-2-2000000000000000000000000000000000000
χ6844-44-4-44-4-20000-4-444222-22-2-20000002-200002-200−2i32i3−2i32i30000000000000000000000000000000000000000000000
χ6944-44-4-44-4-20000-4-444222-22-2-20000002-200002-2002i3−2i32i3−2i30000000000000000000000000000000000000000000000
χ7044-4-44-4-44-244-4-40000-2-2222-2200000000-2-22200000000−2i22i2−2i22i2000000i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ7144-4-44-4-44-244-4-40000-2-2222-2200000000-2-222000000002i2−2i22i2−2i2000000−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ7244-4-44-4-44-2-4-4440000-2-2222-220000000022-2-200000000−2i22i22i2−2i2000000i2i2−i2−i2−i2−i2i2i20000000000000000000000000000
χ7344-4-44-4-44-2-4-4440000-2-2222-220000000022-2-2000000002i2−2i2−2i22i2000000−i2−i2i2i2i2i2−i2−i20000000000000000000000000000
χ744-444-4-4-44400004-44-44-444-4-4-4000000440000-4-40000000000000000000000000000000000000000000000000000
χ754-444-4-4-44-200004-44-4-22-2-2222000000-2-200002200−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ764-444-4-4-44-200004-44-4-22-2-2222000000-2-2000022002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ774-444-4-4-44-20000-44-44-22-2-22224i−4i4i−4i00220000-2-2000000000000−2i2i−2i2i000000000000000000000000000000000000
χ784-444-4-4-44-20000-44-44-22-2-2222−4i4i−4i4i00220000-2-20000000000002i−2i2i−2i000000000000000000000000000000000000
χ794-44-44-44-444i−4i−4i4i0000-444-4-4-44000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ804-44-44-44-44−4i4i4i−4i0000-444-4-4-4400000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ814-44-44-44-4-24i−4i−4i4i00002-2-2222-200000000−2i2i2i−2i0000000000000000006−6−66i6−i6−i6i60000000000000000000000000000
χ824-44-44-44-4-24i−4i−4i4i00002-2-2222-200000000−2i2i2i−2i000000000000000000−666−6−i6i6i6−i60000000000000000000000000000
χ834-44-44-44-4-2−4i4i4i−4i00002-2-2222-2000000002i−2i−2i2i0000000000000000006−6−66−i6i6i6−i60000000000000000000000000000
χ844-44-44-44-4-2−4i4i4i−4i00002-2-2222-2000000002i−2i−2i2i000000000000000000−666−6i6−i6−i6i60000000000000000000000000000
χ854-4-4444-4-4-24i−4i4i−4i4-4-442-22-2-22200004i−4i-22−2i2i−2i2i2-20000000000−2i2i0000000000000000000000000000000000000000
χ864-4-4444-4-4-2−4i4i−4i4i4-4-442-22-2-2220000−4i4i-222i−2i2i−2i2-200000000002i−2i0000000000000000000000000000000000000000
χ874-4-4-4-44444000000004-4-4-44-44000000000000000000000000000000000000000000000022−22−22220000000000000000
χ884-4-4-4-44444000000004-4-4-44-440000000000000000000000000000000000000000000000−222222−220000000000000000
χ89888-8-88-8-8-40000000044-44-4-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8-8888-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000

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