Finite Group Databasebeta

← Group #70893

Character table — Group #70893

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11112222333311112222333322224444666622224444666622224444666644448888121212124444888812121212
order1244361212888822446612128888444412121212888888882424242488888888242424248888224466121288884444121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ311-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i
χ411-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii
χ51-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ3
χ61-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ3
χ71-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ
χ81-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ
χ92222-1-1-1-100002222-1-1-1-100002222-1-1-1-100002222-1-1-1-100002222-1-1-1-100002222-1-1-1-100002222-1-1-1-10000
χ1022-2-2-1-111000022-2-2-1-111000022-2-2-1-111000022-2-2-1-111000022-2-2-1-111000022-2-2-1-111000022-2-2-1-1110000
χ112-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii0000
χ122-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i0000
χ13111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1411111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1511-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i-1-111-1-111−i−iii-1-111-1-111−i−iii
χ1611-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii-1-111-1-111ii−i−i-1-111-1-111ii−i−i
χ171-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ3-11−ii-11−ii−ζζ−ζ3ζ3-11−ii-11−ii−ζζ−ζ3ζ3
χ181-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ3-11−ii-11−iiζ−ζζ3−ζ3-11−ii-11−iiζ−ζζ3−ζ3
χ191-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ-11i−i-11i−i−ζ3ζ3−ζζ-11i−i-11i−i−ζ3ζ3−ζζ
χ201-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ-11i−i-11i−iζ3−ζ3ζ−ζ-11i−i-11i−iζ3−ζ3ζ−ζ
χ212222-1-1-1-100002222-1-1-1-100002222-1-1-1-100002222-1-1-1-100002222-1-1-1-10000-2-2-2-211110000-2-2-2-211110000
χ2222-2-2-1-111000022-2-2-1-111000022-2-2-1-111000022-2-2-1-111000022-2-2-1-1110000-2-22211-1-10000-2-22211-1-10000
χ232-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii0000-22−2i2i1-1i−i0000-22−2i2i1-1i−i0000
χ242-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i0000-222i−2i1-1−ii0000-222i−2i1-1−ii0000
χ25111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ2611111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ2711-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i-1-111-1-111−i−iii-1-111-1-111−i−iii11-1-111-1-1ii−i−i-1-111-1-111−i−iii
χ2811-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii-1-111-1-111ii−i−i-1-111-1-111ii−i−i11-1-111-1-1−i−iii-1-111-1-111ii−i−i
χ291-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ3-11−ii-11−ii−ζζ−ζ3ζ3-11−ii-11−ii−ζζ−ζ3ζ31-1i−i1-1i−iζ−ζζ3−ζ3-11−ii-11−ii−ζζ−ζ3ζ3
χ301-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ3-11−ii-11−iiζ−ζζ3−ζ3-11−ii-11−iiζ−ζζ3−ζ31-1i−i1-1i−i−ζζ−ζ3ζ3-11−ii-11−iiζ−ζζ3−ζ3
χ311-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ-11i−i-11i−i−ζ3ζ3−ζζ-11i−i-11i−i−ζ3ζ3−ζζ1-1−ii1-1−iiζ3−ζ3ζ−ζ-11i−i-11i−i−ζ3ζ3−ζζ
χ321-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ-11i−i-11i−iζ3−ζ3ζ−ζ-11i−i-11i−iζ3−ζ3ζ−ζ1-1−ii1-1−ii−ζ3ζ3−ζζ-11i−i-11i−iζ3−ζ3ζ−ζ
χ332222-1-1-1-100002222-1-1-1-100002222-1-1-1-10000-2-2-2-211110000-2-2-2-2111100002222-1-1-1-10000-2-2-2-211110000
χ3422-2-2-1-111000022-2-2-1-111000022-2-2-1-1110000-2-22211-1-10000-2-22211-1-1000022-2-2-1-1110000-2-22211-1-10000
χ352-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii0000-22−2i2i1-1i−i0000-22−2i2i1-1i−i00002-22i−2i-11−ii0000-22−2i2i1-1i−i0000
χ362-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i0000-222i−2i1-1−ii0000-222i−2i1-1−ii00002-2−2i2i-11i−i0000-222i−2i1-1−ii0000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ3811111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ3911-1-111-1-1ii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−i-1-111-1-111−i−iii-1-111-1-111−i−iii-1-111-1-111−i−iii11-1-111-1-1ii−i−i
χ4011-1-111-1-1−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii-1-111-1-111ii−i−i-1-111-1-111ii−i−i-1-111-1-111ii−i−i11-1-111-1-1−i−iii
χ411-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ3-11−ii-11−ii−ζζ−ζ3ζ3-11−ii-11−ii−ζζ−ζ3ζ3-11−ii-11−ii−ζζ−ζ3ζ31-1i−i1-1i−iζ−ζζ3−ζ3
χ421-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ3-11−ii-11−iiζ−ζζ3−ζ3-11−ii-11−iiζ−ζζ3−ζ3-11−ii-11−iiζ−ζζ3−ζ31-1i−i1-1i−i−ζζ−ζ3ζ3
χ431-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζ-11i−i-11i−i−ζ3ζ3−ζζ-11i−i-11i−i−ζ3ζ3−ζζ-11i−i-11i−i−ζ3ζ3−ζζ1-1−ii1-1−iiζ3−ζ3ζ−ζ
χ441-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ1-1−ii1-1−ii−ζ3ζ3−ζζ-11i−i-11i−iζ3−ζ3ζ−ζ-11i−i-11i−iζ3−ζ3ζ−ζ-11i−i-11i−iζ3−ζ3ζ−ζ1-1−ii1-1−ii−ζ3ζ3−ζζ
χ452222-1-1-1-100002222-1-1-1-100002222-1-1-1-10000-2-2-2-211110000-2-2-2-211110000-2-2-2-2111100002222-1-1-1-10000
χ4622-2-2-1-111000022-2-2-1-111000022-2-2-1-1110000-2-22211-1-10000-2-22211-1-10000-2-22211-1-1000022-2-2-1-1110000
χ472-22i−2i-11−ii00002-22i−2i-11−ii00002-22i−2i-11−ii0000-22−2i2i1-1i−i0000-22−2i2i1-1i−i0000-22−2i2i1-1i−i00002-22i−2i-11−ii0000
χ482-2−2i2i-11i−i00002-2−2i2i-11i−i00002-2−2i2i-11i−i0000-222i−2i1-1−ii0000-222i−2i1-1−ii0000-222i−2i1-1−ii00002-2−2i2i-11i−i0000
χ49222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ5022222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ5122-2-222-2-22i2i−2i−2i22-2-222-2-22i2i−2i−2i-2-222-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
χ5222-2-222-2-2−2i−2i2i2i22-2-222-2-2−2i−2i2i2i-2-222-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ532-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ32-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ3-22−2i2i-22−2i2i−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000000000000000
χ542-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ32-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ3-22−2i2i-22−2i2i2ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000000000000000
χ552-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ2-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ-222i−2i-222i−2i−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000000000000000
χ562-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ2-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ-222i−2i-222i−2i2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000000000000000
χ574444-2-2-2-200004444-2-2-2-20000-4-4-4-422220000000000000000000000000000000000000000000000000000
χ5844-4-4-2-222000044-4-4-2-2220000-4-44422-2-20000000000000000000000000000000000000000000000000000
χ594-44i−4i-22−2i2i00004-44i−4i-22−2i2i0000-44−4i4i2-22i−2i0000000000000000000000000000000000000000000000000000
χ604-4−4i4i-222i−2i00004-4−4i4i-222i−2i0000-444i−4i2-2−2i2i0000000000000000000000000000000000000000000000000000
χ61222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000i2i2i2i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2000000000000000000000000
χ6222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000
χ6322-2-222-2-22i2i−2i−2i-2-222-2-222−2i−2i2i2i000000000000i2i2−i2−i2i2i2−i2−i2−2−222−i2−i2i2i2−i2−i2i2i222−2−2000000000000000000000000
χ6422-2-222-2-2−2i−2i2i2i-2-222-2-2222i2i−2i−2i000000000000i2i2−i2−i2i2i2−i2−i222−2−2−i2−i2i2i2−i2−i2i2i2−2−222000000000000000000000000
χ652-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ3-22−2i2i-22−2i2i−2ζ2ζ−2ζ32ζ3000000000000i2−i2−22i2−i2−22−1+i1−i−1−i1+i−i2i22−2−i2i22−21−i−1+i1+i−1−i000000000000000000000000
χ662-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ3-22−2i2i-22−2i2i2ζ−2ζ2ζ3−2ζ3000000000000i2−i2−22i2−i2−221−i−1+i1+i−1−i−i2i22−2−i2i22−2−1+i1−i−1−i1+i000000000000000000000000
χ672-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ-222i−2i-222i−2i−2ζ32ζ3−2ζ2ζ000000000000i2−i22−2i2−i22−2−1−i1+i−1+i1−i−i2i2−22−i2i2−221+i−1−i1−i−1+i000000000000000000000000
χ682-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ-222i−2i-222i−2i2ζ3−2ζ32ζ−2ζ000000000000i2−i22−2i2−i22−21+i−1−i1−i−1+i−i2i2−22−i2i2−22−1−i1+i−1+i1−i000000000000000000000000
χ694444-2-2-2-20000-4-4-4-4222200000000000000002i22i22i22i2−i2−i2−i2−i20000−2i2−2i2−2i2−2i2i2i2i2i20000000000000000000000000000
χ7044-4-4-2-2220000-4-44422-2-200000000000000002i22i2−2i2−2i2−i2−i2i2i20000−2i2−2i22i22i2i2i2−i2−i20000000000000000000000000000
χ714-44i−4i-22−2i2i0000-44−4i4i2-22i−2i00000000000000002i2−2i2−2222−i2i22−20000−2i22i222−22i2−i2−220000000000000000000000000000
χ724-4−4i4i-222i−2i0000-444i−4i2-2−2i2i00000000000000002i2−2i222−22−i2i2−220000−2i22i2−2222i2−i22−20000000000000000000000000000
χ73222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2i2i2i2i2000000000000000000000000
χ7422222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000
χ7522-2-222-2-22i2i−2i−2i-2-222-2-222−2i−2i2i2i000000000000−i2−i2i2i2−i2−i2i2i222−2−2i2i2−i2−i2i2i2−i2−i2−2−222000000000000000000000000
χ7622-2-222-2-2−2i−2i2i2i-2-222-2-2222i2i−2i−2i000000000000−i2−i2i2i2−i2−i2i2i2−2−222i2i2−i2−i2i2i2−i2−i222−2−2000000000000000000000000
χ772-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ3-22−2i2i-22−2i2i−2ζ2ζ−2ζ32ζ3000000000000−i2i22−2−i2i22−21−i−1+i1+i−1−ii2−i2−22i2−i2−22−1+i1−i−1−i1+i000000000000000000000000
χ782-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ3-22−2i2i-22−2i2i2ζ−2ζ2ζ3−2ζ3000000000000−i2i22−2−i2i22−2−1+i1−i−1−i1+ii2−i2−22i2−i2−221−i−1+i1+i−1−i000000000000000000000000
χ792-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ-222i−2i-222i−2i−2ζ32ζ3−2ζ2ζ000000000000−i2i2−22−i2i2−221+i−1−i1−i−1+ii2−i22−2i2−i22−2−1−i1+i−1+i1−i000000000000000000000000
χ802-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ-222i−2i-222i−2i2ζ3−2ζ32ζ−2ζ000000000000−i2i2−22−i2i2−22−1−i1+i−1+i1−ii2−i22−2i2−i22−21+i−1−i1−i−1+i000000000000000000000000
χ814444-2-2-2-20000-4-4-4-422220000000000000000−2i2−2i2−2i2−2i2i2i2i2i200002i22i22i22i2−i2−i2−i2−i20000000000000000000000000000
χ8244-4-4-2-2220000-4-44422-2-20000000000000000−2i2−2i22i22i2i2i2−i2−i200002i22i2−2i2−2i2−i2−i2i2i20000000000000000000000000000
χ834-44i−4i-22−2i2i0000-44−4i4i2-22i−2i0000000000000000−2i22i222−22i2−i2−2200002i2−2i2−2222−i2i22−20000000000000000000000000000
χ844-4−4i4i-222i−2i0000-444i−4i2-2−2i2i0000000000000000−2i22i2−2222i2−i22−200002i2−2i222−22−i2i2−220000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.