Finite Group Databasebeta

← Group #10868026

Character table — Group #10868026

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244888812121212121212121212242424242424242444448888888844121212122444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1111-1-111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-111-1-1
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-1-111111-1-1
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-11-1-111111-1-1-1-1-111
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-1-1-11-1-11111
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-11-111-1-1111-111-1-1-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1-1111-1-1-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-11-1-1-11111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-111111-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11-1-1111-1-1-1-1-11111
χ17222222222-22222-2-2-22222222-2-200002222-2-2-2-20000000000-2-2000000000000222200000000000000-200-2000000
χ18222222222-22222-2-2-22222222-2-200002222-2-2-2-20000000000-2-2000000000000-2-2-2-2000000000000002002000000
χ19222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-200000000002200000000000022-2-200000000000000200-2000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000000022000000000000-2-22200000000000000-2002000000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-222221111-1-11111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-222-2-2111111-1-1-1-1-1-1-1-11111000000000000-2211-1-10000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-222111111-1-1-1-11111-1-1-1-10000000000002-2-1-1110000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2-1-1-1-1111111-1-1-1-111110000000000002-2-1-1110000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-222-1-1-1-11111111111-1-1-1-1000000000000-2211-1-10000000000
χ2922-2-22-2-22222i2i−2i−2i-2-222-2-2-222-22i−2i00002i2i−2i−2i2-22-200000000002i−2i00000000000000000000000000000002i−2i0002-200
χ3022-2-22-2-22222i2i−2i−2i-2-222-2-2-222-22i−2i00002i2i−2i−2i2-22-200000000002i−2i0000000000000000000000000000000−2i2i000-2200
χ3122-2-22-2-2222−2i−2i2i2i-2-222-2-2-222-2−2i2i0000−2i−2i2i2i2-22-20000000000−2i2i00000000000000000000000000000002i−2i000-2200
χ3222-2-22-2-2222−2i−2i2i2i-2-222-2-2-222-2−2i2i0000−2i−2i2i2i2-22-20000000000−2i2i0000000000000000000000000000000−2i2i0002-200
χ3322-2-22-2-222-22i2i−2i−2i22-22-2-2-222-2−2i2i2i2i−2i−2i2i2i−2i−2i-22-222-2000022-2-2−2i2i2i2i−2i−2i000000000000000000000000000000000000
χ3422-2-22-2-222-22i2i−2i−2i22-22-2-2-222-2−2i2i−2i−2i2i2i2i2i−2i−2i-22-22-220000-2-222−2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3522-2-22-2-222-2−2i−2i2i2i22-22-2-2-222-22i−2i2i2i−2i−2i−2i−2i2i2i-22-22-220000-2-2222i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3622-2-22-2-222-2−2i−2i2i2i22-22-2-2-222-22i−2i−2i−2i2i2i−2i−2i2i2i-22-222-2000022-2-22i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3722-2-22-2-22-1-22i2i−2i−2i22-2-1111-1-11−2i2i2i2i−2i−2i−i−iii1-11-12-20000-1-111i−i−i−iii−i3−i3i3i333−3−300000000000000−i3i33−30000000000
χ3822-2-22-2-22-1-22i2i−2i−2i22-2-1111-1-11−2i2i2i2i−2i−2i−i−iii1-11-12-20000-1-111i−i−i−iiii3i3−i3−i3−3−33300000000000000i3−i3−330000000000
χ3922-2-22-2-22-1-22i2i−2i−2i22-2-1111-1-11−2i2i−2i−2i2i2i−i−iii1-11-1-22000011-1-1i−iii−i−i−i3−i3i3i333−3−300000000000000i3−i3−330000000000
χ4022-2-22-2-22-1-22i2i−2i−2i22-2-1111-1-11−2i2i−2i−2i2i2i−i−iii1-11-1-22000011-1-1i−iii−i−ii3i3−i3−i3−3−33300000000000000−i3i33−30000000000
χ4122-2-22-2-22-1-2−2i−2i2i2i22-2-1111-1-112i−2i2i2i−2i−2iii−i−i1-11-1-22000011-1-1−ii−i−iii−i3−i3i3i3−3−33300000000000000i3−i33−30000000000
χ4222-2-22-2-22-1-2−2i−2i2i2i22-2-1111-1-112i−2i2i2i−2i−2iii−i−i1-11-1-22000011-1-1−ii−i−iiii3i3−i3−i333−3−300000000000000−i3i3−330000000000
χ4322-2-22-2-22-1-2−2i−2i2i2i22-2-1111-1-112i−2i−2i−2i2i2iii−i−i1-11-12-20000-1-111−iiii−i−i−i3−i3i3i3−3−33300000000000000−i3i3−330000000000
χ4422-2-22-2-22-1-2−2i−2i2i2i22-2-1111-1-112i−2i−2i−2i2i2iii−i−i1-11-12-20000-1-111−iiii−i−ii3i3−i3−i333−3−300000000000000i3−i33−30000000000
χ452-22-22-22-22-200002-22-222-2-22-2002i−2i2i−2i0000-2-2220000000000002i−2i2i−2i000000000000000022-2-2000000000000002i−2i
χ462-22-22-22-22-200002-22-222-2-22-2002i−2i2i−2i0000-2-2220000000000002i−2i2i−2i0000000000000000-2-22200000000000000−2i2i
χ472-22-22-22-22-200002-22-222-2-22-200−2i2i−2i2i0000-2-222000000000000−2i2i−2i2i000000000000000022-2-200000000000000−2i2i
χ482-22-22-22-22-200002-22-222-2-22-200−2i2i−2i2i0000-2-222000000000000−2i2i−2i2i0000000000000000-2-222000000000000002i−2i
χ492-2-2222-2-22200002-2-2-2-2-22-222002-2-2200002-2-220000000000002-2-220000000000002i2i−2i−2i000000000000002i−2i0000
χ502-2-2222-2-22200002-2-2-2-2-22-222002-2-2200002-2-220000000000002-2-22000000000000−2i−2i2i2i00000000000000−2i2i0000
χ512-2-2222-2-22200002-2-2-2-2-22-22200-222-200002-2-22000000000000-222-20000000000002i2i−2i−2i00000000000000−2i2i0000
χ522-2-2222-2-22200002-2-2-2-2-22-22200-222-200002-2-22000000000000-222-2000000000000−2i−2i2i2i000000000000002i−2i0000
χ532-2-2-2-2222202-22-200022-22-2-2-20000002-22-20000002−22−200000000002−22−22−22−22i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ542-2-2-2-2222202-22-200022-22-2-2-20000002-22-20000002−22−200000000002−22−22−22−2−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ552-2-2-2-2222202-22-200022-22-2-2-20000002-22-2000000−22−220000000000−22−22−22−222i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ562-2-2-2-2222202-22-200022-22-2-2-20000002-22-2000000−22−220000000000−22−22−22−22−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ572-2-2-2-222220-22-2200022-22-2-2-2000000-22-220000002−2−2200000000002−22−2−22−222i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ582-2-2-2-222220-22-2200022-22-2-2-2000000-22-220000002−2−2200000000002−22−2−22−22−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ592-2-2-2-222220-22-2200022-22-2-2-2000000-22-22000000−222−20000000000−22−222−22−22i−2i−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ602-2-2-2-222220-22-2200022-22-2-2-2000000-22-22000000−222−20000000000−22−222−22−2−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-40000-2-2-2-222220000000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000222222220000000000-2-20000000000000000000000000000000000000000
χ63444-4-44-4-4400000000-4-4444-4-400000000000000000000000000000000000000000022−22−222200000000000000000000
χ64444-4-44-4-4400000000-4-4444-4-4000000000000000000000000000000000000000000−222222−2200000000000000000000
χ6544-44-4-44-4400000000-44-4-44-440000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ6644-44-4-44-4400000000-44-4-44-4400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ6744-4-44-4-44-244i4i−4i−4i-4-44-2222-2-224i−4i0000−2i−2i2i2i-22-220000000000−2i2i0000000000000000000000000000000000000000
χ6844-4-44-4-44-24−4i−4i4i4i-4-44-2222-2-22−4i4i00002i2i−2i−2i-22-2200000000002i−2i0000000000000000000000000000000000000000
χ694-444-4-4-44404i−4i−4i4i0004-44-4-4-440000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ704-444-4-4-4440−4i4i4i−4i0004-44-4-4-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ714-444-4-4-44-204i−4i−4i4i000-22-2222-2000000−2i2i2i−2i00000000000000000000i6−i6−i6i6−666−60000000000000000000000000000
χ724-444-4-4-44-204i−4i−4i4i000-22-2222-2000000−2i2i2i−2i00000000000000000000−i6i6i6−i66−6−660000000000000000000000000000
χ734-444-4-4-44-20−4i4i4i−4i000-22-2222-20000002i−2i−2i2i00000000000000000000i6−i6−i6i66−6−660000000000000000000000000000
χ744-444-4-4-44-20−4i4i4i−4i000-22-2222-20000002i−2i−2i2i00000000000000000000−i6i6i6−i6−666−60000000000000000000000000000
χ754-44-44-44-4440000-44-4-444-4-44-4000000000044-4-40000000000000000000000000000000000000000000000000000
χ764-44-44-44-4-240000-44-42-2-222-220000000000-2-222000000−2i32i3−2i32i3000000000000000000000000000000000000000000
χ774-44-44-44-4-240000-44-42-2-222-220000000000-2-2220000002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ784-44-44-44-4-2-400004-442-2-222-22004i−4i4i−4i000022-2-2000000000000−2i2i−2i2i000000000000000000000000000000000000
χ794-44-44-44-4-2-400004-442-2-222-2200−4i4i−4i4i000022-2-20000000000002i−2i2i−2i000000000000000000000000000000000000
χ804-4-4444-4-44-40000-444-4-4-44-4440000000000-444-40000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-2400004-4-4222-22-2-2004-4-440000-222-2000000000000-222-2000000000000000000000000000000000000
χ824-4-4444-4-4-2400004-4-4222-22-2-200-444-40000-222-20000000000002-2-22000000000000000000000000000000000000
χ834-4-4444-4-4-2-40000-444222-22-2-200000000002-2-22000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ844-4-4444-4-4-2-40000-444222-22-2-200000000002-2-220000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ854-4-4-4-4444-204-44-4000-2-22-2222000000-22-2200000022−2222−220000000000−22−22−22−220000000000000000000000000000
χ864-4-4-4-4444-204-44-4000-2-22-2222000000-22-22000000−2222−222200000000002−22−22−22−20000000000000000000000000000
χ874-4-4-4-4444-20-44-44000-2-22-22220000002-22-200000022−22−22220000000000−22−222−22−20000000000000000000000000000
χ884-4-4-4-4444-20-44-44000-2-22-22220000002-22-2000000−222222−2200000000002−22−2−22−220000000000000000000000000000
χ89888-8-88-8-8-40000000044-4-4-444000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-8-88-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000

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