Finite Group Databasebeta

← Group #10691369

Character table — Group #10691369

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666448888888812121212121212128888888888881212242424242424242424242424242424242222444488884412121212888822
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ91-1-1-111-1111-1111-1-1-1-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-1iiii−i−i−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−ii−iii−i−iii−i−i1-1
χ101-1-1-111-1111-1111-1-1-1-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-1iiii−i−i−i−i-1-1111-1iiii−i−i−i−i-1-1-1-1111111-1-111-1-1ii−i−i−ii−i−iii−i−iii-11
χ111-1-1-111-1111-1111-1-1-1-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-1−i−i−i−iiiii11-1-11-1iiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iiii−iii−i−i−i−iii-11
χ121-1-1-111-1111-1111-1-1-1-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-1−i−i−i−iiiii-1-1111-1iiii−i−i−i−i-1-1-1-11111-1-111-1-111−i−iii−ii−i−iiiii−i−i1-1
χ131-1-1-111-1111-1111-1-1-1-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-1iiii−i−i−i−i11-1-11-1−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−i−ii−i−iiiii−i−i-11
χ141-1-1-111-1111-1111-1-1-1-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-1iiii−i−i−i−i-1-1111-1−i−i−i−iiiii-1-1-1-11111-1-111-1-111ii−i−ii−iii−i−i−i−iii1-1
χ151-1-1-111-1111-1111-1-1-1-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-1−i−i−i−iiiii11-1-11-1−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−ii−i−iii−i−iii1-1
χ161-1-1-111-1111-1111-1-1-1-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-1−i−i−i−iiiii-1-1111-1−i−i−i−iiiii-1-1-1-1111111-1-111-1-1−i−iiii−iii−i−iii−i−i-11
χ1722222222222-2-22-2-222222222-2-2000000002-2-222-22-2000000000000-2-200000000000000002222-2-2-2-20000000000000000
χ1822222222222-2-22-2-222222222-2-2000000002-2-222-22-2000000000000-2-20000000000000000-2-2-2-222220000000000000000
χ19222222222-2-222-222-22222222-2-200000000-222-2-22-22222222220000-2-2000000000000000000000000-2-2-2-2000000000000
χ20222222222-2-222-222-22222222-2-200000000-222-2-22-22-2-2-2-2-2-2-2-20000-2-20000000000000000000000002222000000000000
χ21222222222-2-2-2-2-2-2-2-22222222222i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-2-2-2000000000000222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222222−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-2-2-200000000000022−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i−2i−2i2i2i−2i−2i11111111000000000000-1-1−i−iii−i−iii33−3−333−3−300000000000000−i3i3−i3i3000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i−2i−2i2i2i−2i−2i11111111000000000000-1-1−i−iii−i−iii−3−333−3−33300000000000000i3−i3i3−i3000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i2i2i−2i−2i2i2i11111111000000000000-1-1ii−i−iii−i−i33−3−333−3−300000000000000i3−i3i3−i3000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i2i2i−2i−2i2i2i11111111000000000000-1-1ii−i−iii−i−i−3−333−3−33300000000000000−i3i3−i3i3000000
χ31222-22-2-2-222-200-200222-22-2-2-2002−22−22−22−22002-20-20−i2−i2i2i2−i2−i2i2i20000002−22−22−22−20000000000002i−2i2i−2i−i2i2−i2i2000000000000
χ32222-22-2-2-222-200-200222-22-2-2-2002−22−22−22−22002-20-20i2i2−i2−i2i2i2−i2−i20000002−22−22−22−2000000000000−2i2i−2i2ii2−i2i2−i2000000000000
χ33222-22-2-2-222-200-200222-22-2-2-200−22−22−22−222002-20-20−i2−i2i2i2−i2−i2i2i2000000−22−22−22−22000000000000−2i2i−2i2i−i2i2−i2i2000000000000
χ34222-22-2-2-222-200-200222-22-2-2-200−22−22−22−222002-20-20i2i2−i2−i2i2i2−i2−i2000000−22−22−22−220000000000002i−2i2i−2ii2−i2i2−i2000000000000
χ35222-22-2-2-22-2200200-222-22-2-2-200−i2i2i2−i2−i2i2i2−i2-200-22020−i2−i2i2i2−i2−i2i2i2000000−i2i2i2−i2−i2i2i2−i2000000002-22-20000i2−i2i2−i2000000000000
χ36222-22-2-2-22-2200200-222-22-2-2-200−i2i2i2−i2−i2i2i2−i2-200-22020i2i2−i2−i2i2i2−i2−i2000000−i2i2i2−i2−i2i2i2−i200000000-22-220000−i2i2−i2i2000000000000
χ37222-22-2-2-22-2200200-222-22-2-2-200i2−i2−i2i2i2−i2−i2i2-200-22020−i2−i2i2i2−i2−i2i2i2000000i2−i2−i2i2i2−i2−i2i200000000-22-220000i2−i2i2−i2000000000000
χ38222-22-2-2-22-2200200-222-22-2-2-200i2−i2−i2i2i2−i2−i2i2-200-22020i2i2−i2−i2i2i2−i2−i2000000i2−i2−i2i2i2−i2−i2i2000000002-22-20000−i2i2−i2i2000000000000
χ3922-22-2-2-222002-202-202-22-22-2-2000000000002-20020-22i−2i2i−2i2i−2i2i−2i2−22−200000000002−22−22−22−2000000000000000000−i2i2−i2i200
χ4022-22-2-2-222002-202-202-22-22-2-2000000000002-20020-22i−2i2i−2i2i−2i2i−2i−22−220000000000−22−22−22−22000000000000000000i2−i2i2−i200
χ4122-22-2-2-222002-202-202-22-22-2-2000000000002-20020-2−2i2i−2i2i−2i2i−2i2i2−22−200000000002−22−22−22−2000000000000000000i2−i2i2−i200
χ4222-22-2-2-222002-202-202-22-22-2-2000000000002-20020-2−2i2i−2i2i−2i2i−2i2i−22−220000000000−22−22−22−22000000000000000000−i2i2−i2i200
χ432-22-2-2-2222002-20-220-22-2-22-22000000000002-200-2022-22-2-22-222−2−2200000000002−22−2−22−22000000000000000000−222−200
χ442-22-2-2-2222002-20-220-22-2-22-22000000000002-200-2022-22-2-22-22−222−20000000000−22−222−22−20000000000000000002−2−2200
χ452-22-2-2-2222002-20-220-22-2-22-22000000000002-200-202-22-222-22-22−2−2200000000002−22−2−22−220000000000000000002−2−2200
χ462-22-2-2-2222002-20-220-22-2-22-22000000000002-200-202-22-222-22-2−222−20000000000−22−222−22−2000000000000000000−222−200
χ472-2-222-22-222200-200-2-2-222-2-2200−i2i2−i2i2i2−i2i2−i2200-220-2022−2−2−2−222000000−i2i2−i2i2i2−i2i2−i2000000000000−2i2i2i−2i2−2−22000000000000
χ482-2-222-22-222200-200-2-2-222-2-2200−i2i2−i2i2i2−i2i2−i2200-220-20−2−22222−2−2000000−i2i2−i2i2i2−i2i2−i20000000000002i−2i−2i2i−222−2000000000000
χ492-2-222-22-222200-200-2-2-222-2-2200i2−i2i2−i2−i2i2−i2i2200-220-2022−2−2−2−222000000i2−i2i2−i2−i2i2−i2i20000000000002i−2i−2i2i2−2−22000000000000
χ502-2-222-22-222200-200-2-2-222-2-2200i2−i2i2−i2−i2i2−i2i2200-220-20−2−22222−2−2000000i2−i2i2−i2−i2i2−i2i2000000000000−2i2i2i−2i−222−2000000000000
χ512-2-222-22-22-2-2002002-2-222-2-22002−2−22−222−2-2002-202022−2−2−2−2220000002−2−22−222−2000000002-2-220000−222−2000000000000
χ522-2-222-22-22-2-2002002-2-222-2-22002−2−22−222−2-2002-2020−2−22222−2−20000002−2−22−222−200000000-222-200002−2−22000000000000
χ532-2-222-22-22-2-2002002-2-222-2-2200−222−22−2−22-2002-202022−2−2−2−222000000−222−22−2−2200000000-222-20000−222−2000000000000
χ542-2-222-22-22-2-2002002-2-222-2-2200−222−22−2−22-2002-2020−2−22222−2−2000000−222−22−2−22000000002-2-2200002−2−22000000000000
χ552-2-2-222-2222-2-2-2222-2-2-2-2222-2-22000000002-2-2-2-2222000000000000-22000000000000000022-2-2-2-2220000000000000000
χ562-2-2-222-2222-2-2-2222-2-2-2-2222-2-22000000002-2-2-2-2222000000000000-220000000000000000-2-22222-2-20000000000000000
χ572-2-2-222-222-2222-2-2-22-2-2-2222-2-2200000000-22222-2-2-22i2i2i2i−2i−2i−2i−2i0000-22000000000000000000000000−2i−2i2i2i000000000000
χ582-2-2-222-222-2222-2-2-22-2-2-2222-2-2200000000-22222-2-2-2−2i−2i−2i−2i2i2i2i2i0000-220000000000000000000000002i2i−2i−2i000000000000
χ592-2-2-222-222-22-2-2-2222-2-2-2222-22-222-2-2-2-222-2-2-2222-220000000000002-222-2-2-2-22200000000000000000000000000000000
χ602-2-2-222-222-22-2-2-2222-2-2-2222-22-2-2-22222-2-2-2-2-2222-220000000000002-2-2-22222-2-200000000000000000000000000000000
χ612-2-2-222-22-12-2222-2-2-2111-1-1-112-22i2i2i2i−2i−2i−2i−2i-1-1-1111-110000000022-2-2-11−i−i−i−iiiii-1-1-1-111110000000000002i−2i−i−iii000000
χ622-2-2-222-22-12-2222-2-2-2111-1-1-112-22i2i2i2i−2i−2i−2i−2i-1-1-1111-1100000000-2-222-11−i−i−i−iiiii1111-1-1-1-1000000000000−2i2iii−i−i000000
χ632-2-2-222-22-12-2222-2-2-2111-1-1-112-2−2i−2i−2i−2i2i2i2i2i-1-1-1111-110000000022-2-2-11iiii−i−i−i−i-1-1-1-11111000000000000−2i2iii−i−i000000
χ642-2-2-222-22-12-2222-2-2-2111-1-1-112-2−2i−2i−2i−2i2i2i2i2i-1-1-1111-1100000000-2-222-11iiii−i−i−i−i1111-1-1-1-10000000000002i−2i−i−iii000000
χ652-2-2-222-22-1-22-2-2-2222111-1-1-112-222-2-2-2-222111-1-1-11-1000000000000-11-1-11111-1-133−3−3−3−33300000000000000−333−3000000
χ662-2-2-222-22-1-22-2-2-2222111-1-1-112-222-2-2-2-222111-1-1-11-1000000000000-11-1-11111-1-1−3−33333−3−3000000000000003−3−33000000
χ672-2-2-222-22-1-22-2-2-2222111-1-1-112-2-2-22222-2-2111-1-1-11-1000000000000-1111-1-1-1-11133−3−3−3−333000000000000003−3−33000000
χ682-2-2-222-22-1-22-2-2-2222111-1-1-112-2-2-22222-2-2111-1-1-11-1000000000000-1111-1-1-1-111−3−33333−3−300000000000000−333−3000000
χ6944444444-244-4-44-4-44-2-2-2-2-2-2-2-4-400000000-222-2-22-22000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-444-444-4-2-2-2-2-2-2-2-4-4000000002-2-222-22-2000000000000220000000000000000000000000000000000000000
χ71444-44-4-4-4-24-400-4004-2-22-22220022−2222−2222−2222−22-200-2202000000000000000−22−22−22−2200000000000000000000000000000000
χ72444-44-4-4-4-24-400-4004-2-22-222200−2222−2222−2222−2222-200-22020000000000000002−22−22−22−200000000000000000000000000000000
χ73444-44-4-4-4-2-4400400-4-2-22-222200−2i22i22i2−2i2−2i22i22i2−2i22002-20-2000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ74444-44-4-4-4-2-4400400-4-2-22-2222002i2−2i2−2i22i22i2−2i2−2i22i22002-20-2000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ7544-44-4-4-44400-440-4404-44-44-4-400000000000-4400-404000000000000000000000000000000000000000000000000000000
χ7644-44-4-4-44-2004-404-40-22-22-22200000000000-2200-2020000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ7744-44-4-4-44-2004-404-40-22-22-22200000000000-2200-20200000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ7844-44-4-4-44-200-440-440-22-22-222000000000002-20020-200000000000000000000006−6−666−6−66000000000000000000000000
χ7944-44-4-4-44-200-440-440-22-22-222000000000002-20020-20000000000000000000000−666−6−666−6000000000000000000000000
χ8044-4-4-444-44000000004-4-4-4-44400000000000000000022−22−222222−22−22220000000000000000000000000000000000000000000000
χ8144-4-4-444-44000000004-4-4-4-444000000000000000000−222222−22−222222−220000000000000000000000000000000000000000000000
χ824-444-44-4-4400000000-444-4-44-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ834-444-44-4-4400000000-444-4-44-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ844-44-4-4-444400-4404-40-44-4-44-4400000000000-440040-4000000000000000000000000000000000000000000000000000000
χ854-44-4-4-444-2004-40-4402-222-22-200000000000-220020-20000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ864-44-4-4-444-2004-40-4402-222-22-200000000000-220020-200000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ874-44-4-4-444-200-4404-402-222-22-2000000000002-200-20200000000000000000000006−6−66−666−6000000000000000000000000
χ884-44-4-4-444-200-4404-402-222-22-2000000000002-200-2020000000000000000000000−666−66−6−66000000000000000000000000
χ894-4-444-44-4-24400-400-422-2-222-200−2i22i2−2i22i22i2−2i22i2−2i2-2002-202000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ904-4-444-44-4-24400-400-422-2-222-2002i2−2i22i2−2i2−2i22i2−2i22i2-2002-202000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000
χ914-4-444-44-4-2-4-400400422-2-222-20022−22−2222−222222−22200-220-2000000000000000−222−22−2−2200000000000000000000000000000000
χ924-4-444-44-4-2-4-400400422-2-222-200−222222−2222−22−2222200-220-20000000000000002−2−22−222−200000000000000000000000000000000
χ934-4-4-444-44-24-4-4-4444-4222-2-2-22-4400000000-22222-2-2-20000000000002-20000000000000000000000000000000000000000
χ944-4-4-444-44-2-4444-4-4-44222-2-2-22-44000000002-2-2-2-22220000000000002-20000000000000000000000000000000000000000
χ9588-8-8-888-8-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-88-8-8-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000

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