Finite Group Databasebeta

← Group #10868461

Character table — Group #10868461

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121222666688881212121212122424242424242424444488888888246612124444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ511111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-111111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11111-1-1-1-1-1
χ9111111111-1-1-1-111111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-111-1-1111-1-1
χ10111111111-1-1-1-111111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11-111-1-11-1-111-1-1-111
χ11111111111-1-1-1-111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-11-1-111-111-1-1-1-1111
χ12111111111-1-1-1-111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-11-1-1111-1-11111-1-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-11-1-111-1-1-111-1-1111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-11-1-111111-1-111-1-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-111-1-1-1-1-111111-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-111-1-1111-1-1-1-1-111
χ172222222222222-2-2-2-22222222-2-20000-2-22222-2-20000000000-2-2000000000000222200000000000000-2000000-200
χ182222222222222-2-2-2-22222222-2-20000-2-22222-2-20000000000-2-2000000000000-2-2-2-2000000000000002000000200
χ19222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-200000000002200000000000022-2-2000000000000002000000-200
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000000022000000000000-2-22200000000000000-2000000200
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
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-111111111111100000000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2111122-2-211-1-1-1-1-1-1-1-111110000000000002-2-1-1110000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-21111-2-22211-1-1-1-11111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-1-1-1-122-2-2111111-1-1-1-11111000000000000-2211-1-10000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-1-1-1-1-2-2221111111111-1-1-1-10000000000002-2-1-1110000000000
χ2922-2-2-22-2222i2i−2i−2i2-2-2222-22-2-2-22i−2i2i2i−2i−2i2-22i2i−2i−2i2-22-222-2-200002i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3022-2-2-22-2222i2i−2i−2i2-2-2222-22-2-2-22i−2i−2i−2i2i2i2-22i2i−2i−2i2-2-22-2-22200002i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3122-2-2-22-2222i2i−2i−2i-222-222-22-2-2-2−2i2i0000-222i2i−2i−2i-220000000000−2i2i00000000000000000000000000000002i−2i2-200000
χ3222-2-2-22-2222i2i−2i−2i-222-222-22-2-2-2−2i2i0000-222i2i−2i−2i-220000000000−2i2i0000000000000000000000000000000−2i2i-2200000
χ3322-2-2-22-222−2i−2i2i2i2-2-2222-22-2-2-2−2i2i2i2i−2i−2i2-2−2i−2i2i2i2-2-22-2-2220000−2i2i2i2i−2i−2i000000000000000000000000000000000000
χ3422-2-2-22-222−2i−2i2i2i2-2-2222-22-2-2-2−2i2i−2i−2i2i2i2-2−2i−2i2i2i2-22-222-2-20000−2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3522-2-2-22-222−2i−2i2i2i-222-222-22-2-2-22i−2i0000-22−2i−2i2i2i-2200000000002i−2i00000000000000000000000000000002i−2i-2200000
χ3622-2-2-22-222−2i−2i2i2i-222-222-22-2-2-22i−2i0000-22−2i−2i2i2i-2200000000002i−2i0000000000000000000000000000000−2i2i2-200000
χ3722-2-2-22-22-12i2i−2i−2i2-2-22-1-11-11112i−2i2i2i−2i−2i-11−i−iii-112-2-1-1110000−ii−i−iii33−3−3−i3−i3i3i300000000000000−i3i33−30000000000
χ3822-2-2-22-22-12i2i−2i−2i2-2-22-1-11-11112i−2i2i2i−2i−2i-11−i−iii-112-2-1-1110000−ii−i−iii−3−333i3i3−i3−i300000000000000i3−i3−330000000000
χ3922-2-2-22-22-12i2i−2i−2i2-2-22-1-11-11112i−2i−2i−2i2i2i-11−i−iii-11-2211-1-10000−iiii−i−i33−3−3−i3−i3i3i300000000000000i3−i3−330000000000
χ4022-2-2-22-22-12i2i−2i−2i2-2-22-1-11-11112i−2i−2i−2i2i2i-11−i−iii-11-2211-1-10000−iiii−i−i−3−333i3i3−i3−i300000000000000−i3i33−30000000000
χ4122-2-2-22-22-1−2i−2i2i2i2-2-22-1-11-1111−2i2i2i2i−2i−2i-11ii−i−i-11-2211-1-10000i−i−i−iii33−3−3i3i3−i3−i300000000000000−i3i3−330000000000
χ4222-2-2-22-22-1−2i−2i2i2i2-2-22-1-11-1111−2i2i2i2i−2i−2i-11ii−i−i-11-2211-1-10000i−i−i−iii−3−333−i3−i3i3i300000000000000i3−i33−30000000000
χ4322-2-2-22-22-1−2i−2i2i2i2-2-22-1-11-1111−2i2i−2i−2i2i2i-11ii−i−i-112-2-1-1110000i−iii−i−i33−3−3i3i3−i3−i300000000000000i3−i33−30000000000
χ4422-2-2-22-22-1−2i−2i2i2i2-2-22-1-11-1111−2i2i−2i−2i2i2i-11ii−i−i-112-2-1-1110000i−iii−i−i−3−333−i3−i3i3i300000000000000−i3i3−330000000000
χ452-222-22-2-22000022-2-2-2-2-222-22002-22-22-20000-220000000000002-22-200000000000000002i2i−2i−2i000000000002i−2i000
χ462-222-22-2-22000022-2-2-2-2-222-22002-22-22-20000-220000000000002-22-20000000000000000−2i−2i2i2i00000000000−2i2i000
χ472-222-22-2-22000022-2-2-2-2-222-2200-22-222-20000-22000000000000-22-2200000000000000002i2i−2i−2i00000000000−2i2i000
χ482-222-22-2-22000022-2-2-2-2-222-2200-22-222-20000-22000000000000-22-220000000000000000−2i−2i2i2i000000000002i−2i000
χ492-22-22-2-2222i−2i2i−2i00002-22-22-2-2000000002i−2i2i−2i00000000−i2i22−2000000−i2i2−i2i22−22−22i−2i2-2−i2−i2i2i22−22−20000000000000000
χ502-22-22-2-2222i−2i2i−2i00002-22-22-2-2000000002i−2i2i−2i00000000−i2i22−2000000−i2i2−i2i22−22−2−2i2i-22i2i2−i2−i2−22−220000000000000000
χ512-22-22-2-2222i−2i2i−2i00002-22-22-2-2000000002i−2i2i−2i00000000i2−i2−22000000i2−i2i2−i2−22−222i−2i2-2i2i2−i2−i2−22−220000000000000000
χ522-22-22-2-2222i−2i2i−2i00002-22-22-2-2000000002i−2i2i−2i00000000i2−i2−22000000i2−i2i2−i2−22−22−2i2i-22−i2−i2i2i22−22−20000000000000000
χ532-22-22-2-222−2i2i−2i2i00002-22-22-2-200000000−2i2i−2i2i00000000−i2i2−22000000−i2i2−i2i2−22−222i−2i-22i2i2−i2−i22−22−20000000000000000
χ542-22-22-2-222−2i2i−2i2i00002-22-22-2-200000000−2i2i−2i2i00000000−i2i2−22000000−i2i2−i2i2−22−22−2i2i2-2−i2−i2i2i2−22−220000000000000000
χ552-22-22-2-222−2i2i−2i2i00002-22-22-2-200000000−2i2i−2i2i00000000i2−i22−2000000i2−i2i2−i22−22−22i−2i-22−i2−i2i2i2−22−220000000000000000
χ562-22-22-2-222−2i2i−2i2i00002-22-22-2-200000000−2i2i−2i2i00000000i2−i22−2000000i2−i2i2−i22−22−2−2i2i2-2i2i2−i2−i22−22−20000000000000000
χ572-2-2-2222-2200002-22-2-2-222-22-2002i−2i−2i2i220000-2-20000000000002i−2i−2i2i0000000000002-22-20000000000000000002i−2i
χ582-2-2-2222-2200002-22-2-2-222-22-2002i−2i−2i2i220000-2-20000000000002i−2i−2i2i000000000000-22-22000000000000000000−2i2i
χ592-2-2-2222-2200002-22-2-2-222-22-200−2i2i2i−2i220000-2-2000000000000−2i2i2i−2i0000000000002-22-2000000000000000000−2i2i
χ602-2-2-2222-2200002-22-2-2-222-22-200−2i2i2i−2i220000-2-2000000000000−2i2i2i−2i000000000000-22-220000000000000000002i−2i
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-4000022-2-2-2-2220000000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000222222220000000000-2-20000000000000000000000000000000000000000
χ63444-4-4-44-4400000000-44-4-444-40000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ64444-4-4-44-4400000000-44-4-444-400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ6544-444-4-4-4400000000-444-4-4-44000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ6644-444-4-4-4400000000-444-4-4-440000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6744-4-4-44-44-24i4i−4i−4i-444-4-2-22-2222−4i4i00002-2−2i−2i2i2i2-200000000002i−2i0000000000000000000000000000000000000000
χ6844-4-4-44-44-2−4i−4i4i4i-444-4-2-22-22224i−4i00002-22i2i−2i−2i2-20000000000−2i2i0000000000000000000000000000000000000000
χ694-444-44-4-440000-4-444-4-4-444-44000000-4400004-40000000000000000000000000000000000000000000000000000
χ704-444-44-4-4-2000044-4-4222-2-22-2004-44-4-2200002-2000000000000-22-22000000000000000000000000000000000000
χ714-444-44-4-4-2000044-4-4222-2-22-200-44-44-2200002-20000000000002-22-2000000000000000000000000000000000000
χ724-444-44-4-4-20000-4-444222-2-22-20000002-20000-2200−2i32i3−2i32i30000000000000000000000000000000000000000000000
χ734-444-44-4-4-20000-4-444222-2-22-20000002-20000-22002i3−2i32i3−2i30000000000000000000000000000000000000000000000
χ744-44-44-4-44-24i−4i4i−4i0000-22-22-22200000000−2i2i−2i2i00000000−2i22i222−22000000i2−i2i2−i2−22−220000000000000000000000000000
χ754-44-44-4-44-24i−4i4i−4i0000-22-22-22200000000−2i2i−2i2i000000002i2−2i2−2222000000−i2i2−i2i22−22−20000000000000000000000000000
χ764-44-44-4-44-2−4i4i−4i4i0000-22-22-222000000002i−2i2i−2i00000000−2i22i2−2222000000i2−i2i2−i22−22−20000000000000000000000000000
χ774-44-44-4-44-2−4i4i−4i4i0000-22-22-222000000002i−2i2i−2i000000002i2−2i222−22000000−i2i2−i2i2−22−220000000000000000000000000000
χ784-4-44-4-44444-4-4400004-4-4-4-444000000004-4-44000000000000000000000000000000000000000000000000000000
χ794-4-44-4-4444-444-400004-4-4-4-44400000000-444-4000000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-24-4-440000-22222-2-200000000-222-2000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ814-4-44-4-444-24-4-440000-22222-2-200000000-222-2000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ824-4-44-4-444-2-444-40000-22222-2-2000000002-2-22000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ834-4-44-4-444-2-444-40000-22222-2-2000000002-2-22000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ844-4-4-4444-440000-44-44-4-444-44-4000000-4-40000440000000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-200004-44-422-2-22-22004i−4i−4i4i-2-2000022000000000000−2i2i2i−2i000000000000000000000000000000000000
χ864-4-4-4444-4-200004-44-422-2-22-2200−4i4i4i−4i-2-20000220000000000002i−2i−2i2i000000000000000000000000000000000000
χ874-4-4-4444-4-20000-44-4422-2-22-22000000220000-2-200−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ884-4-4-4444-4-20000-44-4422-2-22-22000000220000-2-2002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ89888-8-8-88-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ9088-888-8-8-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000

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