Finite Group Databasebeta

← Group #72227198

Character table — Group #72227198

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222244444444444444888888888888888888888888888161616161616161616161616161632323232323232323232323232323232323232323232323232323232323232326464646464646464
order122448888244444888816161616888881616161616161616161616161616323232323232323288323232323232323232323232323232323232323232323232323232326464646464646464646464646464646422448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111
χ7111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111
χ8111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1
χ9111111111-1-111-1-111-1-1-1-1-1-1-1ii−i−i11-1-1ii−i−i11ii−i−iiiii−i−i−i−ii−iii−i−i1111-1-1-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ611-1-1ii−i−i
χ10111111111-1-111-1-111-1-1-1-1-1-1-1ii−i−i11-1-1ii−i−i11ii−i−iiiii−i−i−i−ii−iii−i−i1111-1-1-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-1-111−i−iii
χ11111111111-1-111-1-111-1-1-1-1-1-1-1ii−i−i11-1-1ii−i−i11ii−i−iiiii−i−i−i−ii−iii−i−i1111-1-1-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-1-111−i−iii
χ12111111111-1-111-1-111-1-1-1-1-1-1-1ii−i−i11-1-1ii−i−i11ii−i−iiiii−i−i−i−ii−iii−i−i1111-1-1-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ611-1-1ii−i−i
χ13111111111-1-111-1-111-1-1-1-1-1-1-1−i−iii11-1-1−i−iii11−i−iii−i−i−i−iiiii−ii−i−iii1111-1-1-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ211-1-1−i−iii
χ14111111111-1-111-1-111-1-1-1-1-1-1-1−i−iii11-1-1−i−iii11−i−iii−i−i−i−iiiii−ii−i−iii1111-1-1-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-1-111ii−i−i
χ15111111111-1-111-1-111-1-1-1-1-1-1-1−i−iii11-1-1−i−iii11−i−iii−i−i−i−iiiii−ii−i−iii1111-1-1-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-1-111ii−i−i
χ16111111111-1-111-1-111-1-1-1-1-1-1-1−i−iii11-1-1−i−iii11−i−iii−i−i−i−iiiii−ii−i−iii1111-1-1-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ211-1-1−i−iii
χ1711111-1-11111-1-1-1-1-11-1-1-1-1-1-11ii−i−i-1-111ii−i−i11−i−iii−i−i−i−iiiii−iiii−i−i11-1-111-1-1ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ21-11-1i−ii−i
χ1811111-1-11111-1-1-1-1-11-1-1-1-1-1-11ii−i−i-1-111ii−i−i11−i−iii−i−i−i−iiiii−iiii−i−i11-1-111-1-1ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2-11-11−ii−ii
χ1911111-1-11111-1-1-1-1-11-1-1-1-1-1-11ii−i−i-1-111ii−i−i11−i−iii−i−i−i−iiiii−iiii−i−i11-1-111-1-1−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2-11-11−ii−ii
χ2011111-1-11111-1-1-1-1-11-1-1-1-1-1-11ii−i−i-1-111ii−i−i11−i−iii−i−i−i−iiiii−iiii−i−i11-1-111-1-1−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ21-11-1i−ii−i
χ2111111-1-11111-1-1-1-1-11-1-1-1-1-1-11−i−iii-1-111−i−iii11ii−i−iiiii−i−i−i−ii−i−i−iii11-1-111-1-1ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ61-11-1−ii−ii
χ2211111-1-11111-1-1-1-1-11-1-1-1-1-1-11−i−iii-1-111−i−iii11ii−i−iiiii−i−i−i−ii−i−i−iii11-1-111-1-1ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6-11-11i−ii−i
χ2311111-1-11111-1-1-1-1-11-1-1-1-1-1-11−i−iii-1-111−i−iii11ii−i−iiiii−i−i−i−ii−i−i−iii11-1-111-1-1−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6-11-11i−ii−i
χ2411111-1-11111-1-1-1-1-11-1-1-1-1-1-11−i−iii-1-111−i−iii11ii−i−iiiii−i−i−i−ii−i−i−iii11-1-111-1-1−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ61-11-1−ii−ii
χ2511111-1-111-1-1-1-111-11111111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ2611111-1-111-1-1-1-111-11111111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ2711111-1-111-1-1-1-111-11111111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ2811111-1-111-1-1-1-111-11111111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ2911111-1-111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11-111-1
χ3011111-1-111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-111-11-1-11
χ3111111-1-111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-111-11-1-11
χ3211111-1-111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-11-111-1
χ33222222222222222222222222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-22222-2-2-2-222-2-2-2-222222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ352222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000220000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ362222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000220000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ372222222222222222222-2-2-2-22-2-2-2-2-2-2-2-22222-2-2222200000000-2-200000000000000000000000000002−22−22−22−2−22−22−22−2200000000
χ382222222222222222222-2-2-2-22-2-2-2-2-2-2-2-22222-2-2222200000000-2-20000000000000000000000000000−22−22−22−222−22−22−22−200000000
χ39222222222-2-222-2-222-2-22222-22i2i−2i−2i-2-222−2i−2i2i2i-2-2−2i−2i2i2i000000002i−2i00000000000000000000000000001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00000000
χ40222222222-2-222-2-222-2-22222-22i2i−2i−2i-2-222−2i−2i2i2i-2-2−2i−2i2i2i000000002i−2i0000000000000000000000000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i00000000
χ41222222222-2-222-2-222-2-22222-2−2i−2i2i2i-2-2222i2i−2i−2i-2-22i2i−2i−2i00000000−2i2i00000000000000000000000000001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00000000
χ42222222222-2-222-2-222-2-22222-2−2i−2i2i2i-2-2222i2i−2i−2i-2-22i2i−2i−2i00000000−2i2i0000000000000000000000000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00000000
χ43222222222-2-222-2-222-2-2-2-2-2-2-22i2i−2i−2i22-2-22i2i−2i−2i222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i−2i−2i−2i2i2i-2-2-2-222220000000000000000000000000000000000000000
χ44222222222-2-222-2-222-2-2-2-2-2-2-2−2i−2i2i2i22-2-2−2i−2i2i2i22−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i−2i2i2i2i−2i−2i-2-2-2-222220000000000000000000000000000000000000000
χ4522222-2-22222-2-2-2-2-22-2-2222222i2i−2i−2i22-2-2−2i−2i2i2i-2-22i2i−2i−2i00000000−2i2i00000000000000000000000000001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i00000000
χ4622222-2-22222-2-2-2-2-22-2-2222222i2i−2i−2i22-2-2−2i−2i2i2i-2-22i2i−2i−2i00000000−2i2i0000000000000000000000000000−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i00000000
χ4722222-2-22222-2-2-2-2-22-2-222222−2i−2i2i2i22-2-22i2i−2i−2i-2-2−2i−2i2i2i000000002i−2i00000000000000000000000000001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i00000000
χ4822222-2-22222-2-2-2-2-22-2-222222−2i−2i2i2i22-2-22i2i−2i−2i-2-2−2i−2i2i2i000000002i−2i0000000000000000000000000000−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i00000000
χ4922222-2-22222-2-2-2-2-22-2-2-2-2-2-222i2i−2i−2i-2-2222i2i−2i−2i22−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i−2i2i−2i−2i2i2i-2-222-2-2220000000000000000000000000000000000000000
χ5022222-2-22222-2-2-2-2-22-2-2-2-2-2-22−2i−2i2i2i-2-222−2i−2i2i2i222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i−2i2i2i−2i−2i-2-222-2-2220000000000000000000000000000000000000000
χ5122222-2-222-2-2-2-222-22222222-22222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000
χ5222222-2-222-2-2-2-222-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2222222-2-22222-2-20000000000000000000000000000000000000000
χ5322222-2-222-2-2-2-222-2222-2-2-2-2-222222222-2-2-2-2-2-2222200000000-2-200000000000000000000000000002−2−22−222−2−222−22−2−2200000000
χ5422222-2-222-2-2-2-222-2222-2-2-2-2-222222222-2-2-2-2-2-2222200000000-2-20000000000000000000000000000−222−22−2−222−2−22−222−200000000
χ5522222-2-222-2-2-2-222-2222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-200000000220000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ5622222-2-222-2-2-2-222-2222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-200000000220000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ5722-22-200-2-200002i−2i022i−2i2i2i−2i−2i02ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ62-200002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6000000002-22i−2i00ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5ζ+ζ5−ζ−ζ5000000000000000000000000
χ5822-22-200-2-200002i−2i022i−2i2i2i−2i−2i02ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ62-200002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6000000002-22i−2i00−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5−ζ−ζ5ζ+ζ5000000000000000000000000
χ5922-22-200-2-200002i−2i022i−2i2i2i−2i−2i02ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ62-20000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ600000000-22−2i2i00ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5−ζ+ζ5ζ−ζ5000000000000000000000000
χ6022-22-200-2-200002i−2i022i−2i2i2i−2i−2i02ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ62-20000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ600000000-22−2i2i00−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5ζ−ζ5−ζ+ζ5000000000000000000000000
χ6122-22-200-2-200002i−2i022i−2i2i2i−2i−2i0−2ζ22ζ2−2ζ62ζ60000−2ζ22ζ2−2ζ62ζ62-200002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ600000000-22−2i2i00ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5ζ+ζ5−ζ−ζ5000000000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.