Finite Group Databasebeta

← Group #10868071

Character table — Group #10868071

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
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111-1-1-1111-1-1-11111-1-1
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1111-1-1-1-111
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1111-1-11-1-1-111-1-111
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1111-1-1-1111-1-111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1111-1-11-111-1-1-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-11-1-11111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-1-1111-111-1-111-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-111-11-1-111-1-111
χ17222222222-22222-2-2-22222222-2-200002222-2-2-2-20000000000-2-2000000000000222200000000000000-2-200000000
χ18222222222-22222-2-2-22222222-2-200002222-2-2-2-20000000000-2-2000000000000-2-2-2-2000000000000002200000000
χ19222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-200000000002200000000000022-2-200000000000000-2200000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000000022000000000000-2-222000000000000002-200000000
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
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-222-2-2111111-1-1-1-1-1-1-1-111110000000000002-211-1-10000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-222111111-1-1-1-11111-1-1-1-1000000000000-22-1-1110000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2-1-1-1-1111111-1-1-1-11111000000000000-22-1-1110000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-222-1-1-1-11111111111-1-1-1-10000000000002-211-1-10000000000
χ2922-22-2-2-222-200002-2222-2-2-22-2002i2i−2i−2i0000-2-2220000000000002i2i−2i−2i000000000000000022-2-20000000000002i−2i00
χ3022-22-2-2-222-200002-2222-2-2-22-2002i2i−2i−2i0000-2-2220000000000002i2i−2i−2i0000000000000000-2-222000000000000−2i2i00
χ3122-22-2-2-222-200002-2222-2-2-22-200−2i−2i2i2i0000-2-222000000000000−2i−2i2i2i000000000000000022-2-2000000000000−2i2i00
χ3222-22-2-2-222-200002-2222-2-2-22-200−2i−2i2i2i0000-2-222000000000000−2i−2i2i2i0000000000000000-2-2220000000000002i−2i00
χ332-222-22-2-22200002-2-2-2-2-22-222002-22-200002-22-20000000000002-22-20000000000002i2i−2i−2i0000000000000000002i−2i
χ342-222-22-2-22200002-2-2-2-2-22-222002-22-200002-22-20000000000002-22-2000000000000−2i−2i2i2i000000000000000000−2i2i
χ352-222-22-2-22200002-2-2-2-2-22-22200-22-2200002-22-2000000000000-22-220000000000002i2i−2i−2i000000000000000000−2i2i
χ362-222-22-2-22200002-2-2-2-2-22-22200-22-2200002-22-2000000000000-22-22000000000000−2i−2i2i2i0000000000000000002i−2i
χ372-22-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i0000002−2−i2i2000000000022−2−2−i2−i2i2i22i−2i2-22−22−2−i2i2−i2i20000000000000000
χ382-22-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i0000002−2−i2i2000000000022−2−2−i2−i2i2i2−2i2i-22−22−22i2−i2i2−i20000000000000000
χ392-22-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i000000−22i2−i20000000000−2−222i2i2−i2−i22i−2i2-2−22−22i2−i2i2−i20000000000000000
χ402-22-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i000000−22i2−i20000000000−2−222i2i2−i2−i2−2i2i-222−22−2−i2i2−i2i20000000000000000
χ412-22-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i0000002−2i2−i2000000000022−2−2i2i2−i2−i22i−2i-22−22−22−i2i2−i2i20000000000000000
χ422-22-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i0000002−2i2−i2000000000022−2−2i2i2−i2−i2−2i2i2-22−22−2i2−i2i2−i20000000000000000
χ432-22-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i000000−22−i2i20000000000−2−222−i2−i2i2i22i−2i-222−22−2i2−i2i2−i20000000000000000
χ442-22-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i000000−22−i2i20000000000−2−222−i2−i2i2i2−2i2i2-2−22−22−i2i2−i2i20000000000000000
χ452-2-222-22-2222i−2i2i−2i-2-22-2-22-222-22i−2i00002i−2i2i−2i2-2-2200000000002i−2i000000000000000000000000000000002-22i−2i0000
χ462-2-222-22-2222i−2i2i−2i-2-22-2-22-222-22i−2i00002i−2i2i−2i2-2-2200000000002i−2i00000000000000000000000000000000-22−2i2i0000
χ472-2-222-22-222−2i2i−2i2i-2-22-2-22-222-2−2i2i0000−2i2i−2i2i2-2-220000000000−2i2i000000000000000000000000000000002-2−2i2i0000
χ482-2-222-22-222−2i2i−2i2i-2-22-2-22-222-2−2i2i0000−2i2i−2i2i2-2-220000000000−2i2i00000000000000000000000000000000-222i−2i0000
χ492-2-222-22-22-22i−2i2i−2i22-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i2i−2i-222-22-2000022-2-2−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ502-2-222-22-22-22i−2i2i−2i22-2-2-22-222-2−2i2i−2i2i2i−2i2i−2i2i−2i-222-2-220000-2-222−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ512-2-222-22-22-2−2i2i−2i2i22-2-2-22-222-22i−2i2i−2i−2i2i−2i2i−2i2i-222-2-220000-2-2222i−2i2i−2i−2i2i000000000000000000000000000000000000
χ522-2-222-22-22-2−2i2i−2i2i22-2-2-22-222-22i−2i−2i2i2i−2i−2i2i−2i2i-222-22-2000022-2-22i−2i−2i2i2i−2i000000000000000000000000000000000000
χ532-2-222-22-2-1-22i−2i2i−2i22-211-11-1-11−2i2i2i−2i−2i2i−ii−ii1-1-112-20000-1-111i−i−iii−i−i3i3−i3i33−33−300000000000000−i3i33−30000000000
χ542-2-222-22-2-1-22i−2i2i−2i22-211-11-1-11−2i2i2i−2i−2i2i−ii−ii1-1-112-20000-1-111i−i−iii−ii3−i3i3−i3−33−3300000000000000i3−i3−330000000000
χ552-2-222-22-2-1-22i−2i2i−2i22-211-11-1-11−2i2i−2i2i2i−2i−ii−ii1-1-11-22000011-1-1i−ii−i−ii−i3i3−i3i33−33−300000000000000i3−i3−330000000000
χ562-2-222-22-2-1-22i−2i2i−2i22-211-11-1-11−2i2i−2i2i2i−2i−ii−ii1-1-11-22000011-1-1i−ii−i−iii3−i3i3−i3−33−3300000000000000−i3i33−30000000000
χ572-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-112i−2i2i−2i−2i2ii−ii−i1-1-11-22000011-1-1−ii−iii−i−i3i3−i3i3−33−3300000000000000i3−i33−30000000000
χ582-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-112i−2i2i−2i−2i2ii−ii−i1-1-11-22000011-1-1−ii−iii−ii3−i3i3−i33−33−300000000000000−i3i3−330000000000
χ592-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-112i−2i−2i2i2i−2ii−ii−i1-1-112-20000-1-111−iii−i−ii−i3i3−i3i3−33−3300000000000000−i3i3−330000000000
χ602-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-112i−2i−2i2i2i−2ii−ii−i1-1-112-20000-1-111−iii−i−iii3−i3i3−i33−33−300000000000000i3−i33−30000000000
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
χ63444-4-4-44-4400000000-44-4-44-44000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ64444-4-4-44-4400000000-44-4-44-440000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6544-44-4-4-44440000-44-444-4-4-44-4000000000044-4-40000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44-240000-44-4-2-2222-220000000000-2-222000000−2i32i3−2i32i3000000000000000000000000000000000000000000
χ6744-44-4-4-44-240000-44-4-2-2222-220000000000-2-2220000002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ6844-44-4-4-44-2-400004-44-2-2222-22004i4i−4i−4i000022-2-2000000000000−2i−2i2i2i000000000000000000000000000000000000
χ6944-44-4-4-44-2-400004-44-2-2222-2200−4i−4i4i4i000022-2-20000000000002i2i−2i−2i000000000000000000000000000000000000
χ7044-4-444-4-4404-4-44000-4444-4-4-40000004-4-4400000000000000000000000000000000000000000000000000000000
χ7144-4-444-4-440-444-4000-4444-4-4-4000000-444-400000000000000000000000000000000000000000000000000000000
χ7244-4-444-4-4-204-4-440002-2-2-2222000000-222-200000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ7344-4-444-4-4-204-4-440002-2-2-2222000000-222-200000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ7444-4-444-4-4-20-444-40002-2-2-22220000002-2-2200000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ7544-4-444-4-4-20-444-40002-2-2-22220000002-2-2200000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ764-444-44-4-44-40000-444-4-4-44-4440000000000-44-440000000000000000000000000000000000000000000000000000
χ774-444-44-4-4-2400004-4-4222-22-2-2004-44-40000-22-22000000000000-22-22000000000000000000000000000000000000
χ784-444-44-4-4-2400004-4-4222-22-2-200-44-440000-22-220000000000002-22-2000000000000000000000000000000000000
χ794-444-44-4-4-2-40000-444222-22-2-200000000002-22-2000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ804-444-44-4-4-2-40000-444222-22-2-200000000002-22-20000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ814-44-44-4-44-204i4i−4i−4i000-22-2222-2000000−2i−2i2i2i00000022−22−2i22i20000000000−2−222i2i2−i2−i20000000000000000000000000000
χ824-44-44-4-44-204i4i−4i−4i000-22-2222-2000000−2i−2i2i2i000000−22222i2−2i2000000000022−2−2−i2−i2i2i20000000000000000000000000000
χ834-44-44-4-44-20−4i−4i4i4i000-22-2222-20000002i2i−2i−2i00000022−222i2−2i20000000000−2−222−i2−i2i2i20000000000000000000000000000
χ844-44-44-4-44-20−4i−4i4i4i000-22-2222-20000002i2i−2i−2i000000−2222−2i22i2000000000022−2−2i2i2−i2−i20000000000000000000000000000
χ854-4-444-44-4-244i−4i4i−4i-4-4422-22-2-224i−4i0000−2i2i−2i2i-222-20000000000−2i2i0000000000000000000000000000000000000000
χ864-4-444-44-4-24−4i4i−4i4i-4-4422-22-2-22−4i4i00002i−2i2i−2i-222-200000000002i−2i0000000000000000000000000000000000000000
χ874-4-4-4-44444000000004-4-444-4-40000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ884-4-4-4-44444000000004-4-444-4-400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ89888-8-8-88-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8-8888-400000000-444-4-444000000000000000000000000000000000000000000000000000000000000000000

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