Finite Group Databasebeta

← Group #11709162

Character table — Group #11709162

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111111111111111166666666121212121212121212121212121212121616161616161616161616161616161616161616161616161616161616161616
order122244444444444422444444888888888888888833666666121212121212121212121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ31111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ511111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ611111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ711-1-111-1-1iiii−i−i−i−i1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i111-1-11-1-111-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i
χ811-1-111-1-1iiii−i−i−i−i1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11−1+i32−1+i321−i321−i32ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7
χ911-1-111-1-1iiii−i−i−i−i1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11
χ1011-1-111-1-1−i−i−i−iiiii1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii111-1-11-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii
χ1111-1-111-1-1−i−i−i−iiiii1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ11ζ11−1+i32−1+i321−i321−i32−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ7ζ7
χ1211-1-111-1-1−i−i−i−iiiii1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ7ζ7−1−i32−1−i321+i321+i32−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ11ζ11
χ132222-2-2-2-222-2-222-2-2222-22-2-2-20000000000000000-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-111-1-1
χ142222-2-2-2-222-2-222-2-2222-22-2-2-200000000000000001+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ152222-2-2-2-222-2-222-2-2222-22-2-2-200000000000000001−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ162222-2-2-2-2-2-222-2-22222-22-22-2-20000000000000000-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-111-1-111
χ172222-2-2-2-2-2-222-2-22222-22-22-2-200000000000000001+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ182222-2-2-2-2-2-222-2-22222-22-22-2-200000000000000001−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ1922-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i-220000000000000000-1-1-111-11111-1-1ii−i−i−i−iii11-1-1ii−i−i−i−iii
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χ2122-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i-2200000000000000001−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ2222-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2−2i2i2i−2i-220000000000000000-1-1-111-11111-1-1−i−iiiii−i−i11-1-1−i−iiiii−i−i
χ2322-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2−2i2i2i−2i-2200000000000000001+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ2422-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2−2i2i2i−2i-2200000000000000001−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ25333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ263333333333333333-1-1-1-1-1-1-1-111−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i00000000000000000000000000000000
χ273333333333333333-1-1-1-1-1-1-1-111−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i00000000000000000000000000000000
χ283333333333333333-1-1-1-1-1-1-1-1−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i1100000000000000000000000000000000
χ293333333333333333-1-1-1-1-1-1-1-1−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i1100000000000000000000000000000000
χ3033333333-3-3-3-3-3-3-3-333-3-3-3-333-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
χ3133333333-3-3-3-3-3-3-3-3-1-11111-1-111−1+2i−1−2i11−1+2i−1−2i-1-11−2i1+2i-1-11−2i1+2i00000000000000000000000000000000
χ3233333333-3-3-3-3-3-3-3-3-1-11111-1-111−1−2i−1+2i11−1−2i−1+2i-1-11+2i1−2i-1-11+2i1−2i00000000000000000000000000000000
χ3333333333-3-3-3-3-3-3-3-3-1-11111-1-1−1+2i−1−2i11−1+2i−1−2i111−2i1+2i-1-11−2i1+2i-1-100000000000000000000000000000000
χ3433333333-3-3-3-3-3-3-3-3-1-11111-1-1−1−2i−1+2i11−1−2i−1+2i111+2i1−2i-1-11+2i1−2i-1-100000000000000000000000000000000
χ3533-3-333-3-33i3i3i3i−3i−3i−3i−3i3-33i3i−3i−3i3-3-1-1-1-11111−i−i−i−iiiii00000000000000000000000000000000
χ3633-3-333-3-33i3i3i3i−3i−3i−3i−3i-11−i−iii-1111−1+2i−1−2i-1-11−2i1+2iii−2−i2−i−i−i2+i−2+i00000000000000000000000000000000
χ3733-3-333-3-33i3i3i3i−3i−3i−3i−3i-11−i−iii-1111−1−2i−1+2i-1-11+2i1−2iii2−i−2−i−i−i−2+i2+i00000000000000000000000000000000
χ3833-3-333-3-33i3i3i3i−3i−3i−3i−3i-11−i−iii-11−1+2i−1−2i111−2i1+2i-1-1−2−i2−iii2+i−2+i−i−i00000000000000000000000000000000
χ3933-3-333-3-33i3i3i3i−3i−3i−3i−3i-11−i−iii-11−1−2i−1+2i111+2i1−2i-1-12−i−2−iii−2+i2+i−i−i00000000000000000000000000000000
χ4033-3-333-3-3−3i−3i−3i−3i3i3i3i3i3-3−3i−3i3i3i3-3-1-1-1-11111iiii−i−i−i−i00000000000000000000000000000000
χ4133-3-333-3-3−3i−3i−3i−3i3i3i3i3i-11ii−i−i-1111−1+2i−1−2i-1-11−2i1+2i−i−i2+i−2+iii−2−i2−i00000000000000000000000000000000
χ4233-3-333-3-3−3i−3i−3i−3i3i3i3i3i-11ii−i−i-1111−1−2i−1+2i-1-11+2i1−2i−i−i−2+i2+iii2−i−2−i00000000000000000000000000000000
χ4333-3-333-3-3−3i−3i−3i−3i3i3i3i3i-11ii−i−i-11−1+2i−1−2i111−2i1+2i-1-12+i−2+i−i−i−2−i2−iii00000000000000000000000000000000
χ4433-3-333-3-3−3i−3i−3i−3i3i3i3i3i-11ii−i−i-11−1−2i−1+2i111+2i1−2i-1-1−2+i2+i−i−i2−i−2−iii00000000000000000000000000000000
χ454-44-44i−4i4i−4i4-44i−4i4-44i−4i00000000000000000000000011-11-1-11-1i−ii−ii−i1-1i−i1-1i−ii−ii−i1-1i−i1-1
χ464-44-44i−4i4i−4i4-44i−4i4-44i−4i000000000000000000000000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ11−ζ11−1−i321+i32ζ11−ζ11−1−i321+i32ζ7−ζ7ζ7−ζ7ζ7−ζ7−1+i321−i32ζ7−ζ7−1+i321−i32
χ474-44-44i−4i4i−4i4-44i−4i4-44i−4i000000000000000000000000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ7−ζ7−1+i321−i32ζ7−ζ7−1+i321−i32ζ11−ζ11ζ11−ζ11ζ11−ζ11−1−i321+i32ζ11−ζ11−1−i321+i32
χ484-44-44i−4i4i−4i-44−4i4i-44−4i4i00000000000000000000000011-11-1-11-1i−ii−i−ii-11−ii-11i−ii−i−ii-11−ii-11
χ494-44-44i−4i4i−4i-44−4i4i-44−4i4i000000000000000000000000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32ζ11−ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−ζ11ζ111+i32−1−i32ζ7−ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−ζ7ζ71−i32−1+i32
χ504-44-44i−4i4i−4i-44−4i4i-44−4i4i000000000000000000000000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32ζ7−ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−ζ7ζ71−i32−1+i32ζ11−ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−ζ11ζ111+i32−1−i32
χ514-44-4−4i4i−4i4i4-4−4i4i4-4−4i4i00000000000000000000000011-11-1-11-1−ii−ii−ii1-1−ii1-1−ii−ii−ii1-1−ii1-1
χ524-44-4−4i4i−4i4i4-4−4i4i4-4−4i4i000000000000000000000000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−1−i321+i32−ζ11ζ11−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−1+i321−i32−ζ7ζ7−1+i321−i32
χ534-44-4−4i4i−4i4i4-4−4i4i4-4−4i4i000000000000000000000000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−1+i321−i32−ζ7ζ7−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−1−i321+i32−ζ11ζ11−1−i321+i32
χ544-44-4−4i4i−4i4i-444i−4i-444i−4i00000000000000000000000011-11-1-11-1−ii−iii−i-11i−i-11−ii−iii−i-11i−i-11
χ554-44-4−4i4i−4i4i-444i−4i-444i−4i000000000000000000000000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−ζ11ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32ζ11−ζ111+i32−1−i32−ζ7ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32ζ7−ζ71−i32−1+i32
χ564-44-4−4i4i−4i4i-444i−4i-444i−4i000000000000000000000000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−ζ7ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32ζ7−ζ71−i32−1+i32−ζ11ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32ζ11−ζ111+i32−1−i32
χ574-4-444i−4i−4i4i4i−4i-44−4i4i4-400000000000000000000000011-1-11-1-11i−i−ii-11i−i1-1−iii−i−ii-11i−i1-1−ii
χ584-4-444i−4i−4i4i4i−4i-44−4i4i4-4000000000000000000000000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32ζ11−ζ11−ζ11ζ111+i32−1−i32ζ11−ζ11−1−i321+i32−ζ11ζ11ζ7−ζ7−ζ7ζ71−i32−1+i32ζ7−ζ7−1+i321−i32−ζ7ζ7
χ594-4-444i−4i−4i4i4i−4i-44−4i4i4-4000000000000000000000000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32ζ7−ζ7−ζ7ζ71−i32−1+i32ζ7−ζ7−1+i321−i32−ζ7ζ7ζ11−ζ11−ζ11ζ111+i32−1−i32ζ11−ζ11−1−i321+i32−ζ11ζ11
χ604-4-444i−4i−4i4i−4i4i4-44i−4i-4400000000000000000000000011-1-11-1-11i−i−ii1-1−ii-11i−ii−i−ii1-1−ii-11i−i
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χ624-4-444i−4i−4i4i−4i4i4-44i−4i-44000000000000000000000000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32ζ7−ζ7−ζ7ζ7−1+i321−i32−ζ7ζ71−i32−1+i32ζ7−ζ7ζ11−ζ11−ζ11ζ11−1−i321+i32−ζ11ζ111+i32−1−i32ζ11−ζ11
χ634-4-44−4i4i4i−4i4i−4i4-4−4i4i-4400000000000000000000000011-1-11-1-11−iii−i1-1i−i-11−ii−iii−i1-1i−i-11−ii
χ644-4-44−4i4i4i−4i4i−4i4-4−4i4i-44000000000000000000000000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−1−i321+i32ζ11−ζ111+i32−1−i32−ζ11ζ11−ζ7ζ7ζ7−ζ7−1+i321−i32ζ7−ζ71−i32−1+i32−ζ7ζ7
χ654-4-44−4i4i4i−4i4i−4i4-4−4i4i-44000000000000000000000000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−1+i321−i32ζ7−ζ71−i32−1+i32−ζ7ζ7−ζ11ζ11ζ11−ζ11−1−i321+i32ζ11−ζ111+i32−1−i32−ζ11ζ11
χ664-4-44−4i4i4i−4i−4i4i-444i−4i4-400000000000000000000000011-1-11-1-11−iii−i-11−ii1-1i−i−iii−i-11−ii1-1i−i
χ674-4-44−4i4i4i−4i−4i4i-444i−4i4-4000000000000000000000000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−ζ11ζ11ζ11−ζ111+i32−1−i32−ζ11ζ11−1−i321+i32ζ11−ζ11−ζ7ζ7ζ7−ζ71−i32−1+i32−ζ7ζ7−1+i321−i32ζ7−ζ7
χ684-4-44−4i4i4i−4i−4i4i-444i−4i4-4000000000000000000000000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−ζ7ζ7ζ7−ζ71−i32−1+i32−ζ7ζ7−1+i321−i32ζ7−ζ7−ζ11ζ11ζ11−ζ111+i32−1−i32−ζ11ζ11−1−i321+i32ζ11−ζ11
χ696666-6-6-6-666-6-666-6-6-2-2-22-2222000000000000000000000000000000000000000000000000
χ706666-6-6-6-6-6-666-6-666-2-22-22-222000000000000000000000000000000000000000000000000
χ7166-6-6-6-6666i6i−6i−6i−6i−6i6i6i-22−2i2i2i−2i2-2000000000000000000000000000000000000000000000000
χ7266-6-6-6-666−6i−6i6i6i6i6i−6i−6i-222i−2i−2i2i2-2000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.