Finite Group Databasebeta

← Group #10694246

Character table — Group #10694246

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666448888888812121212121212124444444488881212242424242424242424242424242424244444888888884412121212888822
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ10111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-111−i−iii-11
χ11111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1−i−iii-11
χ12111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-111ii−i−i1-1
χ13111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i-11
χ14111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-1−i−iii1-1
χ15111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii1-1
χ16111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1ii−i−i-11
χ1722222222222-2-2-222-22222222-2-200000000222-2-2-22-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ1822222222222-2-2-222-22222222-2-200000000222-2-2-22-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2-2222-2-222222222-2-200000000-2-2-2222-222222-2-2-2-20000-2-20000000000000000-2-22200000000000000000000
χ20222222222-2-2222-2-222222222-2-200000000-2-2-2222-22-2-2-2-222220000-2-2000000000000000022-2-200000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i11111111000000002i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i1111111100000000−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i11111111000000002i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i1111111100000000−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
χ29222-2-2-2-2222-222-22-2-2-2-2-2-22222-2000000002-2-222-22-20000000000002-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ30222-2-2-2-2222-222-22-2-2-2-2-2-22222-2000000002-2-222-22-20000000000002-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ31222-2-2-2-2222-2-2-222-22-2-2-2-2222-2222-2-222-2-22-2-2-2-2222000000000000-2222-2-222-2-200000000000000000000000000000000
χ32222-2-2-2-2222-2-2-222-22-2-2-2-2222-22-2-222-2-2222-2-2-2-2222000000000000-22-2-222-2-22200000000000000000000000000000000
χ33222-2-2-2-222-2222-2-22-2-2-2-2-2222-222i2i−2i−2i−2i−2i2i2i-22222-2-2-2000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ34222-2-2-2-222-2222-2-22-2-2-2-2-2222-22−2i−2i2i2i2i2i−2i−2i-22222-2-2-2000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ35222-2-2-2-222-22-2-22-222-2-2-2-22222-200000000-222-2-22-220000000000002-20000000000000000000022-2-2-2-222000000000000
χ36222-2-2-2-222-22-2-22-222-2-2-2-22222-200000000-222-2-22-220000000000002-200000000000000000000-2-22222-2-2000000000000
χ37222-2-2-2-22-12-2-2-222-221111-1-1-1-2222-2-222-2-2-11111-1-1-10000000000001-1-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ38222-2-2-2-22-12-2-2-222-221111-1-1-1-2222-2-222-2-2-11111-1-1-10000000000001-1-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ39222-2-2-2-22-12-2-2-222-221111-1-1-1-22-2-222-2-222-11111-1-1-10000000000001-111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ40222-2-2-2-22-12-2-2-222-221111-1-1-1-22-2-222-2-222-11111-1-1-10000000000001-111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ41222-2-2-2-22-1-2222-2-22-21111-1-1-1-222i2i−2i−2i−2i−2i2i2i1-1-1-1-11110000000000001-1−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i3000000
χ42222-2-2-2-22-1-2222-2-22-21111-1-1-1-222i2i−2i−2i−2i−2i2i2i1-1-1-1-11110000000000001-1−i−iiiii−i−i−3−33333−3−300000000000000i3−i3−i3i3000000
χ43222-2-2-2-22-1-2222-2-22-21111-1-1-1-22−2i−2i2i2i2i2i−2i−2i1-1-1-1-11110000000000001-1ii−i−i−i−iii33−3−3−3−33300000000000000i3−i3−i3i3000000
χ44222-2-2-2-22-1-2222-2-22-21111-1-1-1-22−2i−2i2i2i2i2i−2i−2i1-1-1-1-11110000000000001-1ii−i−i−i−iii−3−33333−3−300000000000000−i3i3i3−i3000000
χ4522-222-2-2-222-2000-22022-2-22-2-2000000000022-2000-202i2i−2i−2i2i2i−2i−2i2−22−200000000002−22−22−22−2000000000000000000−i2i2−i2i200
χ4622-222-2-2-222-2000-22022-2-22-2-2000000000022-2000-202i2i−2i−2i2i2i−2i−2i−22−220000000000−22−22−22−22000000000000000000i2−i2i2−i200
χ4722-222-2-2-222-2000-22022-2-22-2-2000000000022-2000-20−2i−2i2i2i−2i−2i2i2i2−22−200000000002−22−22−22−2000000000000000000i2−i2i2−i200
χ4822-222-2-2-222-2000-22022-2-22-2-2000000000022-2000-20−2i−2i2i2i−2i−2i2i2i−22−220000000000−22−22−22−22000000000000000000−i2i2−i2i200
χ4922-222-2-2-22-220002-2022-2-22-2-20000000000-2-22000202i2i−2i−2i−2i−2i2i2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000−222−200
χ5022-222-2-2-22-220002-2022-2-22-2-20000000000-2-22000202i2i−2i−2i−2i−2i2i2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000002−2−2200
χ5122-222-2-2-22-220002-2022-2-22-2-20000000000-2-2200020−2i−2i2i2i2i2i−2i−2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000002−2−2200
χ5222-222-2-2-22-220002-2022-2-22-2-20000000000-2-2200020−2i−2i2i2i2i2i−2i−2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000−222−200
χ532-2-22-22-222002-2200-22-22-2-2-2200−i2i2−i2i2−i2i2−i2i20002-220-200002-22-2000000−i2i2−i2i2−i2i2−i2i2000000002-200−i2i2−i2i2−i2i2−i2i2000000000000
χ542-2-22-22-222002-2200-22-22-2-2-2200−i2i2−i2i2−i2i2−i2i20002-220-20000-22-22000000−i2i2−i2i2−i2i2−i2i200000000-2200i2−i2i2−i2i2−i2i2−i2000000000000
χ552-2-22-22-222002-2200-22-22-2-2-2200i2−i2i2−i2i2−i2i2−i20002-220-200002-22-2000000i2−i2i2−i2i2−i2i2−i2000000002-200i2−i2i2−i2i2−i2i2−i2000000000000
χ562-2-22-22-222002-2200-22-22-2-2-2200i2−i2i2−i2i2−i2i2−i20002-220-20000-22-22000000i2−i2i2−i2i2−i2i2−i200000000-2200−i2i2−i2i2−i2i2−i2i2000000000000
χ572-2-22-22-22200-22-20022-22-2-2-22002−22−2−22−22000-22-20200002-22-20000002−22−2−22−2200000000-2200−22−222−22−2000000000000
χ582-2-22-22-22200-22-20022-22-2-2-22002−22−2−22−22000-22-2020000-22-220000002−22−2−22−22000000002-2002−22−2−22−22000000000000
χ592-2-22-22-22200-22-20022-22-2-2-2200−22−222−22−2000-22-20200002-22-2000000−22−222−22−200000000-22002−22−2−22−22000000000000
χ602-2-22-22-22200-22-20022-22-2-2-2200−22−222−22−2000-22-2020000-22-22000000−22−222−22−2000000002-200−22−222−22−2000000000000
χ612-2-2-22-2222002-2-2002-22-22-2-22002−2−22−222−20002-2-2022-22-200000000002−2−22−222−200000000002-22−2−222−2−22000000000000
χ622-2-2-22-2222002-2-2002-22-22-2-22002−2−22−222−20002-2-202-22-2200000000002−2−22−222−20000000000-22−222−2−222−2000000000000
χ632-2-2-22-2222002-2-2002-22-22-2-2200−222−22−2−220002-2-2022-22-20000000000−222−22−2−2200000000002-2−222−2−222−2000000000000
χ642-2-2-22-2222002-2-2002-22-22-2-2200−222−22−2−220002-2-202-22-220000000000−222−22−2−220000000000-222−2−222−2−22000000000000
χ652-2-2-22-222200-22200-2-22-22-2-2200−i2i2i2−i2−i2i2i2−i2000-2220-22-22-20000000000−i2i2i2−i2−i2i2i2−i20000000000-22−i2i2i2−i2i2−i2−i2i2000000000000
χ662-2-2-22-222200-22200-2-22-22-2-2200−i2i2i2−i2−i2i2i2−i2000-2220-2-22-220000000000−i2i2i2−i2−i2i2i2−i200000000002-2i2−i2−i2i2−i2i2i2−i2000000000000
χ672-2-2-22-222200-22200-2-22-22-2-2200i2−i2−i2i2i2−i2−i2i2000-2220-22-22-20000000000i2−i2−i2i2i2−i2−i2i20000000000-22i2−i2−i2i2−i2i2i2−i2000000000000
χ682-2-2-22-222200-22200-2-22-22-2-2200i2−i2−i2i2i2−i2−i2i2000-2220-2-22-220000000000i2−i2−i2i2i2−i2−i2i200000000002-2−i2i2i2−i2i2−i2−i2i2000000000000
χ6944444444-244-4-4-444-4-2-2-2-2-2-2-2-4-400000000-2-2-2222-22000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4444-4-44-2-2-2-2-2-2-2-4-400000000222-2-2-22-2000000000000220000000000000000000000000000000000000000
χ71444-4-4-4-44-24-444-44-4-42222-2-2-24-400000000-222-2-22-22000000000000-220000000000000000000000000000000000000000
χ72444-4-4-4-44-2-44-4-44-4442222-2-2-24-4000000002-2-222-22-2000000000000-220000000000000000000000000000000000000000
χ7344-444-4-4-4-24-4000-440-2-222-2220000000000-2-22000200000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ7444-444-4-4-4-24-4000-440-2-222-2220000000000-2-220002000000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ7544-444-4-4-4-2-440004-40-2-222-222000000000022-2000-2000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ7644-444-4-4-4-2-440004-40-2-222-222000000000022-2000-20000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ7744-4-4-444-4444000-4-40-4-4444-4-400000000004-44000-40000000000000000000000000000000000000000000000000000000
χ7844-4-4-444-44-4-4000440-4-4444-4-40000000000-44-400040000000000000000000000000000000000000000000000000000000
χ7944-4-4-444-4-244000-4-4022-2-2-2220000000000-22-2000200000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ8044-4-4-444-4-244000-4-4022-2-2-2220000000000-22-2000200000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ8144-4-4-444-4-2-4-400044022-2-2-22200000000002-22000-2000000000000000000000006−6−66−666−6000000000000000000000000
χ8244-4-4-444-4-2-4-400044022-2-2-22200000000002-22000-200000000000000000000000−666−66−6−66000000000000000000000000
χ834-444-4-44-44000000004-4-44-44-400000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ844-444-4-44-44000000004-4-44-44-40000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ854-44-444-4-4400000000-444-4-44-40000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ864-44-444-4-4400000000-444-4-44-4000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ874-4-44-44-44-2004-4400-4-22-2222-200−2i22i2−2i22i2−2i22i2−2i22i2000-22-20200000000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ884-4-44-44-44-2004-4400-4-22-2222-2002i2−2i22i2−2i22i2−2i22i2−2i2000-22-20200000000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ894-4-44-44-44-200-44-4004-22-2222-20022−2222−22−2222−22220002-220-200000000000000−22−222−22−200000000000000000000000000000000
χ904-4-44-44-44-200-44-4004-22-2222-200−2222−222222−2222−220002-220-2000000000000002−22−2−22−2200000000000000000000000000000000
χ914-4-4-44-444-2004-4-40042-22-222-20022−22−2222−222222−22000-2220-200000000000000−222−22−2−2200000000000000000000000000000000
χ924-4-4-44-444-2004-4-40042-22-222-200−222222−2222−22−2222000-2220-2000000000000002−2−22−222−200000000000000000000000000000000
χ934-4-4-44-444-200-44400-42-22-222-200−2i22i22i2−2i2−2i22i22i2−2i20002-2-20200000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ944-4-4-44-444-200-44400-42-22-222-2002i2−2i2−2i22i22i2−2i2−2i22i20002-2-20200000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ958-888-8-88-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-888-8-8-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000

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