Finite Group Databasebeta

← Group #10855238

Character table — Group #10855238

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order12222222344444444666666644121212121212121222444444666688881212121212122424242424242424444444448888888812121212444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ4111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ9111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-11-1-1-1-11
χ10111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-11111-1
χ11111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-11
χ12111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-111-11-1-11-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-111111111-1-1-1-111-1-11-1-1-11-1
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1111-11
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-1111-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-11-1-1-11
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-20000000000000000-2-200000000000022220000000000000000-2-20000
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-20000000000000000-2-2000000000000-2-2-2-20000000000000000220000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000000002200000000000022-2-20000000000000000-220000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000022000000000000-2-22200000000000000002-20000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-2221111-2-2-2-2-1-11111111111110000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-12222-2-2-2-2-1-1-1-122-2-2111111-1-1-1-111110000000000000000-1-111000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-2-222-1-1-1-1-2-2221111111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22222-2-21111-2-22211-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-2-2-22222111122-2-211-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ2922-2-22-22-220000-22-2222-22-2-2-200-2-200002200002i−2i0000000000002i2i−2i−2i00000000000022-2-22i2i−2i−2i00000000000000
χ3022-2-22-22-220000-22-2222-22-2-2-200-2-200002200002i−2i0000000000002i2i−2i−2i000000000000-2-222−2i−2i2i2i00000000000000
χ3122-2-22-22-220000-22-2222-22-2-2-200-2-20000220000−2i2i000000000000−2i−2i2i2i00000000000022-2-2−2i−2i2i2i00000000000000
χ3222-2-22-22-220000-22-2222-22-2-2-200-2-20000220000−2i2i000000000000−2i−2i2i2i000000000000-2-2222i2i−2i−2i00000000000000
χ332-222-2-22-222i2i−2i−2i2-2-22-2-2222-2-22i−2i2-22i2i−2i−2i2-200000000000000002i−2i00000000000000002-22-2000000000000002i−2i00
χ342-222-2-22-222i2i−2i−2i2-2-22-2-2222-2-22i−2i2-22i2i−2i−2i2-200000000000000002i−2i0000000000000000-22-2200000000000000−2i2i00
χ352-222-2-22-222i2i−2i−2i-222-2-2-2222-2-2−2i2i-222i2i−2i−2i-22002-2002i−2i00000000−2i2i00000000000000000000000000002-22i−2i000000
χ362-222-2-22-222i2i−2i−2i-222-2-2-2222-2-2−2i2i-222i2i−2i−2i-2200-2200−2i2i00000000−2i2i0000000000000000000000000000-22−2i2i000000
χ372-222-2-22-22−2i−2i2i2i2-2-22-2-2222-2-2−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i00000000000000002-22-200000000000000−2i2i00
χ382-222-2-22-22−2i−2i2i2i2-2-22-2-2222-2-2−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i0000000000000000-22-22000000000000002i−2i00
χ392-222-2-22-22−2i−2i2i2i-222-2-2-2222-2-22i−2i-22−2i−2i2i2i-22002-200−2i2i000000002i−2i00000000000000000000000000002-2−2i2i000000
χ402-222-2-22-22−2i−2i2i2i-222-2-2-2222-2-22i−2i-22−2i−2i2i2i-2200-22002i−2i000000002i−2i0000000000000000000000000000-222i−2i000000
χ412-222-2-22-2-12i2i−2i−2i-222-211-1-1-111−2i2i1-1−i−iii1-1002-2002i−2i−i3−i3i3i30000i−i3−33−3−i3−i3i3i333−3−30000000000000000-11−ii000000
χ422-222-2-22-2-12i2i−2i−2i-222-211-1-1-111−2i2i1-1−i−iii1-1002-2002i−2ii3i3−i3−i30000i−i−33−33i3i3−i3−i3−3−3330000000000000000-11−ii000000
χ432-222-2-22-2-12i2i−2i−2i-222-211-1-1-111−2i2i1-1−i−iii1-100-2200−2i2i−i3−i3i3i30000i−i3−33−3i3i3−i3−i3−3−33300000000000000001-1i−i000000
χ442-222-2-22-2-12i2i−2i−2i-222-211-1-1-111−2i2i1-1−i−iii1-100-2200−2i2ii3i3−i3−i30000i−i−33−33−i3−i3i3i333−3−300000000000000001-1i−i000000
χ452-222-2-22-2-1−2i−2i2i2i-222-211-1-1-1112i−2i1-1ii−i−i1-1002-200−2i2i−i3−i3i3i30000−ii−33−33−i3−i3i3i3−3−3330000000000000000-11i−i000000
χ462-222-2-22-2-1−2i−2i2i2i-222-211-1-1-1112i−2i1-1ii−i−i1-1002-200−2i2ii3i3−i3−i30000−ii3−33−3i3i3−i3−i333−3−30000000000000000-11i−i000000
χ472-222-2-22-2-1−2i−2i2i2i-222-211-1-1-1112i−2i1-1ii−i−i1-100-22002i−2i−i3−i3i3i30000−ii−33−33i3i3−i3−i333−3−300000000000000001-1−ii000000
χ482-222-2-22-2-1−2i−2i2i2i-222-211-1-1-1112i−2i1-1ii−i−i1-100-22002i−2ii3i3−i3−i30000−ii3−33−3−i3−i3i3i3−3−33300000000000000001-1−ii000000
χ492-22-222-2-222-22-200002-22-2-22-200002-22-200000000000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2−i2i2i20000000000
χ502-22-222-2-222-22-200002-22-2-22-200002-22-200000000000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2-22-220000i2−i2i2−i2i2i2−i2−i20000000000
χ512-22-222-2-222-22-200002-22-2-22-200002-22-200000000000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2i2−i2−i20000000000
χ522-22-222-2-222-22-200002-22-2-22-200002-22-200000000000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2−i2i2i20000000000
χ532-22-222-2-22-22-2200002-22-2-22-20000-22-2200000000000000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i22-2-220000i2−i2i2−i2−i2−i2i2i20000000000
χ542-22-222-2-22-22-2200002-22-2-22-20000-22-2200000000000000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i2-222-20000−i2i2−i2i2i2i2−i2−i20000000000
χ552-22-222-2-22-22-2200002-22-2-22-20000-22-2200000000000000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i22-2-220000−i2i2−i2i2i2i2−i2−i20000000000
χ562-22-222-2-22-22-2200002-22-2-22-20000-22-2200000000000000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i2-222-20000i2−i2i2−i2−i2−i2i2i20000000000
χ572-2-2-2-222220000-2-222-2-2-22-22200-2200002-22-20000002-22-200000000000000000000002-2-2200002-22-20000000000
χ582-2-2-2-222220000-2-222-2-2-22-22200-2200002-22-20000002-22-20000000000000000000000-222-20000-22-220000000000
χ592-2-2-2-222220000-2-222-2-2-22-22200-2200002-2-22000000-22-2200000000000000000000002-2-220000-22-220000000000
χ602-2-2-2-222220000-2-222-2-2-22-22200-2200002-2-22000000-22-220000000000000000000000-222-200002-22-20000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-4-4-4444i−4i−4i4i0000-444-4-4-4400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-444−4i4i4i−4i0000-444-4-4-440000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ65444-4-4-4-44-24i−4i−4i4i00002-2-2222-20000−2i2i2i−2i0000000000000000000000006−6−66i6−i6−i6i600000000000000000000000000
χ66444-4-4-4-44-24i−4i−4i4i00002-2-2222-20000−2i2i2i−2i000000000000000000000000−666−6−i6i6i6−i600000000000000000000000000
χ67444-4-4-4-44-2−4i4i4i−4i00002-2-2222-200002i−2i−2i2i0000000000000000000000006−6−66−i6i6i6−i600000000000000000000000000
χ68444-4-4-4-44-2−4i4i4i−4i00002-2-2222-200002i−2i−2i2i000000000000000000000000−666−6i6−i6−i6i600000000000000000000000000
χ6944-44-44-4-4400000000-44-4-444-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ7044-44-44-4-4400000000-44-4-444-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ7144-4-44-44-4400004-44-444-44-4-4-400440000-4-400000000000000000000000000000000000000000000000000000000
χ7244-4-44-44-4-200004-44-4-2-22-222200-2-200002200000000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ7344-4-44-44-4-200004-44-4-2-22-222200-2-2000022000000002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ7444-4-44-44-4-20000-44-44-2-22-222200220000-2-200004i−4i000000000000−2i−2i2i2i0000000000000000000000000000000000
χ7544-4-44-44-4-20000-44-44-2-22-222200220000-2-20000−4i4i0000000000002i2i−2i−2i0000000000000000000000000000000000
χ764-444-4-44-4-24i4i−4i−4i4-4-4422-2-2-2224i−4i-22−2i−2i2i2i-220000000000000000−2i2i00000000000000000000000000000000000000
χ774-444-4-44-4-2−4i−4i4i4i4-4-4422-2-2-222−4i4i-222i2i−2i−2i-2200000000000000002i−2i00000000000000000000000000000000000000
χ784-44-444-4-4-24-44-40000-22-222-220000-22-2200000000000000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ794-44-444-4-4-24-44-40000-22-222-220000-22-22000000000000002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ804-44-444-4-4-2-44-440000-22-222-2200002-22-200000000000000−2i22i22i2−2i2000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ814-44-444-4-4-2-44-440000-22-222-2200002-22-2000000000000002i2−2i2−2i22i2000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ824-4-444-4-444000000004-4-4-44-4400000000000000000000000000000000000000000000000022−22−222200000000000000
χ834-4-444-4-444000000004-4-4-44-44000000000000000000000000000000000000000000000000−222222−2200000000000000
χ844-4-4-4-44444000044-4-4-4-4-44-444004-40000-4400000000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-2000044-4-4222-22-2-200-2200002-2000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ864-4-4-4-4444-2000044-4-4222-22-2-200-2200002-20000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ874-4-4-4-4444-20000-4-444222-22-2-2002-20000-224-4000000-22-2200000000000000000000000000000000000000000000
χ884-4-4-4-4444-20000-4-444222-22-2-2002-20000-22-440000002-22-200000000000000000000000000000000000000000000
χ8988-88-88-8-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000

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