Finite Group Databasebeta

← Group #10714441

Character table — Group #10714441

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order122222344446668888121212122424242424242424668812121616161616161616242424244848484848484848484848484848484824668812121616161624242424484848484848484844448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ922222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-22200000000-2-2-2-200000000000000002222-2-2220000-2-2-2-20000000000000000
χ1022222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-22200000000-2-2-2-20000000000000000-2-2-2-222-2-2000022220000000000000000
χ112222222-2-2-2-22220000-2-2-2-2000000002200-2-22222−2−2−2−2000022222222−2−2−2−2−2−2−2−200002i−2i00−i2−i2i2i22i2i−2i−2i−i2−i2−i2−i2i2i2i2i200000000
χ122222222-2-2-2-22220000-2-2-2-2000000002200-2-22222−2−2−2−2000022222222−2−2−2−2−2−2−2−20000−2i2i00i2i2−i2−i2−2i−2i2i2ii2i2i2i2−i2−i2−i2−i200000000
χ132222222-2-2-2-22220000-2-2-2-2000000002200-2-2−2−2−2−222220000−2−2−2−2−2−2−2−22222222200002i−2i00i2i2−i2−i22i2i−2i−2ii2i2i2i2−i2−i2−i2−i200000000
χ142222222-2-2-2-22220000-2-2-2-2000000002200-2-2−2−2−2−222220000−2−2−2−2−2−2−2−2222222220000−2i2i00−i2−i2i2i2−2i−2i2i2i−i2−i2−i2−i2i2i2i2i200000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-211-2-2-2-211111111111100000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-1-122-1-1-2-2-2-2-1-1-1-11111111100000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-211-2-21122221111-1-1-1-1-1-1-1-100000000
χ19222222-12222-1-1-1-2-2-2-2-1-1-1-111111111-1-1-2-2-1-10000000011113333−3−3−3−33333−3−3−3−322-1-1-2-2-1-10000111133−3−333−3−300000000
χ20222222-12222-1-1-1-2-2-2-2-1-1-1-111111111-1-1-2-2-1-10000000011113333−3−3−3−33333−3−3−3−3-2-21122110000-1-1-1-1−3−333−3−33300000000
χ21222222-12222-1-1-1-2-2-2-2-1-1-1-111111111-1-1-2-2-1-1000000001111−3−3−3−33333−3−3−3−3333322-1-1-2-2-1-100001111−3−333−3−33300000000
χ22222222-12222-1-1-1-2-2-2-2-1-1-1-111111111-1-1-2-2-1-1000000001111−3−3−3−33333−3−3−3−33333-2-21122110000-1-1-1-133−3−333−3−300000000
χ23222222-1-2-2-2-2-1-1-1000011113333−3−3−3−3-1-100112222−2−2−2−233−3−3ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ4600−i3i32i−2i−i3i3−i2−i2i2i2−i−iiiζ10+ζ14ζ10+ζ14ζ26+ζ46ζ26+ζ46−ζ10−ζ14−ζ10−ζ14−ζ26−ζ46−ζ26−ζ4600000000
χ24222222-1-2-2-2-2-1-1-1000011113333−3−3−3−3-1-100112222−2−2−2−233−3−3ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ4600i3−i3−2i2ii3−i3i2i2−i2−i2ii−i−i−ζ10−ζ14−ζ10−ζ14−ζ26−ζ46−ζ26−ζ46ζ10+ζ14ζ10+ζ14ζ26+ζ46ζ26+ζ4600000000
χ25222222-1-2-2-2-2-1-1-1000011113333−3−3−3−3-1-10011−2−2−2−2222233−3−3−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ4600−i3i32i−2i−i3i3i2i2−i2−i2−i−iii−ζ10−ζ14−ζ10−ζ14−ζ26−ζ46−ζ26−ζ46ζ10+ζ14ζ10+ζ14ζ26+ζ46ζ26+ζ4600000000
χ26222222-1-2-2-2-2-1-1-1000011113333−3−3−3−3-1-10011−2−2−2−2222233−3−3−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ4600i3−i3−2i2ii3−i3−i2−i2i2i2ii−i−iζ10+ζ14ζ10+ζ14ζ26+ζ46ζ26+ζ46−ζ10−ζ14−ζ10−ζ14−ζ26−ζ46−ζ26−ζ4600000000
χ27222222-1-2-2-2-2-1-1-100001111−3−3−3−33333-1-100112222−2−2−2−2−3−333ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ1400−i3i3−2i2i−i3i3i2i2−i2−i2ii−i−i−ζ26−ζ46−ζ26−ζ46−ζ10−ζ14−ζ10−ζ14ζ26+ζ46ζ26+ζ46ζ10+ζ14ζ10+ζ1400000000
χ28222222-1-2-2-2-2-1-1-100001111−3−3−3−33333-1-100112222−2−2−2−2−3−333ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ1400i3−i32i−2ii3−i3−i2−i2i2i2−i−iiiζ26+ζ46ζ26+ζ46ζ10+ζ14ζ10+ζ14−ζ26−ζ46−ζ26−ζ46−ζ10−ζ14−ζ10−ζ1400000000
χ29222222-1-2-2-2-2-1-1-100001111−3−3−3−33333-1-10011−2−2−2−22222−3−333−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ1400−i3i3−2i2i−i3i3−i2−i2i2i2ii−i−iζ26+ζ46ζ26+ζ46ζ10+ζ14ζ10+ζ14−ζ26−ζ46−ζ26−ζ46−ζ10−ζ14−ζ10−ζ1400000000
χ30222222-1-2-2-2-2-1-1-100001111−3−3−3−33333-1-10011−2−2−2−22222−3−333−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14ζ10−ζ14ζ10−ζ1400i3−i32i−2ii3−i3i2i2−i2−i2−i−iii−ζ26−ζ46−ζ26−ζ46−ζ10−ζ14−ζ10−ζ14ζ26+ζ46ζ26+ζ46ζ10+ζ14ζ10+ζ1400000000
χ312222-2-222-22-22222222222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000000000
χ322222-2-222-22-22222222222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ332222-2-222-22-2222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-20000000022220000000000000000000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000
χ342222-2-222-22-2222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2000000002222000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000
χ352222-2-22-22-222220000-2-2-2-200000000-2-2002222−2−2−2−222000022−2−222−2−2−2−222−2−2222-22200-2-22−2−2200002−22−2−22−2200000000
χ362222-2-22-22-222220000-2-2-2-200000000-2-2002222−2−2−2−222000022−2−222−2−2−2−222−2−222-22-2-20022−222−20000−22−222−22−200000000
χ372222-2-22-22-222220000-2-2-2-200000000-2-20022−2−22222−2−20000−2−222−2−22222−2−222−2−22-22200-2-2−222−20000−22−222−22−200000000
χ382222-2-22-22-222220000-2-2-2-200000000-2-20022−2−22222−2−20000−2−222−2−22222−2−222−2−2-22-2-200222−2−2200002−22−2−22−2200000000
χ392222-2-2-12-22-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111-2-21122-2-222-2-21111-1-111-1-111-1-111-1-11100−i3i300i3−i30000−i3i3−i3i3i3−i3−i3i3i3−i3−i3i300000000
χ402222-2-2-12-22-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111-2-21122-2-222-2-21111-1-111-1-111-1-111-1-11100i3−i300−i3i30000i3−i3i3−i3−i3i3i3−i3−i3i3i3−i300000000
χ412222-2-2-12-22-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111-2-211-2-222-2-222111111-1-111-1-111-1-111-1-100−i3i300i3−i30000−i3i3−i3i3−i3i3i3−i3−i3i3i3−i300000000
χ422222-2-2-12-22-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111-2-211-2-222-2-222111111-1-111-1-111-1-111-1-100i3−i300−i3i30000i3−i3i3−i3i3−i3−i3i3i3−i3−i3i300000000
χ432222-2-2-12-22-2-1-1-1-2-2-2-2-1-1-1-11111111111221100000000-1-1-1-133−3−3−3−33333−3−3−3−33300−i3i300i3−i3−2i2i−2i2ii3−i3i3−i3i−ii−ii−ii−i00000000
χ442222-2-2-12-22-2-1-1-1-2-2-2-2-1-1-1-11111111111221100000000-1-1-1-133−3−3−3−33333−3−3−3−33300i3−i300−i3i32i−2i2i−2i−i3i3−i3i3−ii−ii−ii−ii00000000
χ452222-2-2-12-22-2-1-1-1-2-2-2-2-1-1-1-11111111111221100000000-1-1-1-1−3−33333−3−3−3−33333−3−300−i3i300i3−i32i−2i2i−2ii3−i3i3−i3−ii−ii−ii−ii00000000
χ462222-2-2-12-22-2-1-1-1-2-2-2-2-1-1-1-11111111111221100000000-1-1-1-1−3−33333−3−3−3−33333−3−300i3−i300−i3i3−2i2i−2i2i−i3i3−i3i3i−ii−ii−ii−i00000000
χ472222-2-2-1-22-22-1-1-1000011113333−3−3−3−31100-1-122−2−2−2−222−3−333ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ462-2-1-100112−2−223−3−33ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ4600000000
χ482222-2-2-1-22-22-1-1-1000011113333−3−3−3−31100-1-122−2−2−2−222−3−333ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46-221100-1-1−222−2−333−3−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ4600000000
χ492222-2-2-1-22-22-1-1-1000011113333−3−3−3−31100-1-1−2−22222−2−2−3−333−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ462-2-1-10011−222−23−3−33−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ4600000000
χ502222-2-2-1-22-22-1-1-1000011113333−3−3−3−31100-1-1−2−22222−2−2−3−333−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46-221100-1-12−2−22−333−3ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ4600000000
χ512222-2-2-1-22-22-1-1-100001111−3−3−3−333331100-1-122−2−2−2−22233−3−3ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ142-2-1-100112−2−22−333−3ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14−ζ26+ζ46ζ26−ζ46−ζ10+ζ14ζ10−ζ1400000000
χ522222-2-2-1-22-22-1-1-100001111−3−3−3−333331100-1-122−2−2−2−22233−3−3ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14-221100-1-1−222−23−3−33−ζ26+ζ46ζ26−ζ46−ζ10+ζ14ζ10−ζ14ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ1400000000
χ532222-2-2-1-22-22-1-1-100001111−3−3−3−333331100-1-1−2−22222−2−233−3−3−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ142-2-1-10011−222−2−333−3−ζ26+ζ46ζ26−ζ46−ζ10+ζ14ζ10−ζ14ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ1400000000
χ542222-2-2-1-22-22-1-1-100001111−3−3−3−333331100-1-1−2−22222−2−233−3−3−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14-221100-1-12−2−223−3−33ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14−ζ26+ζ46ζ26−ζ46−ζ10+ζ14ζ10−ζ1400000000
χ552-2-222-22-222-2-2-2222-2-2-2-22222-2-222-2-22-22-22-2000000002-22-2000000000000000000000000000000000000000000002i−2i00
χ562-2-222-22-222-2-2-2222-2-2-2-22222-2-222-2-22-22-22-2000000002-22-200000000000000000000000000000000000000000000−2i2i00
χ572-2-222-22-222-2-2-22-2-222-2-222-2-222-2-2222-2-222-200000000-22-2200000000000000000000000000000000000000002i−2i000000
χ582-2-222-22-222-2-2-22-2-222-2-222-2-222-2-2222-2-222-200000000-22-220000000000000000000000000000000000000000−2i2i000000
χ592-2-22-222-2-222-2-2222-2-2-2-22222-2-222-2-2-22-22-2200000000-22-2200000000000000000000000000000000000000000000002-2
χ602-2-22-222-2-222-2-2222-2-2-2-22222-2-222-2-2-22-22-2200000000-22-220000000000000000000000000000000000000000000000-22
χ612-2-22-222-2-222-2-22-2-222-2-222-2-222-2-222-222-2-22000000002-22-20000000000000000000000000000000000000000002-20000
χ622-2-22-222-2-222-2-22-2-222-2-222-2-222-2-222-222-2-22000000002-22-2000000000000000000000000000000000000000000-220000
χ6344-4-400400004-4-422−2222−22000022−2222−2222−2222−22000000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.