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C47×C3⋊(ΓL(1,𝔽8)⋊C4) #26044892

order11844
isoclinismisoclinic class of C3⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×C3⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC3⋊(C47×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic3×C47)
unambiguous semidirect productDic21⋊(C3×C47)
unambiguous semidirect product(C47×Dic21)⋊C3

Splittings

derivedC3×C7 ⋊ C3×C4×C47
HallC3×ΓL(1,𝔽8)×C47 ⋊ C4
HallC7×C47 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C47
SylowC7 ⋊ C3×Dic3×C47

Subgroups

subgroupG/H
center, hypercenterC2×C47C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C3×C4×C47
FrattiniC2C47×C3⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C47C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C47C2
cosocleC2×C3×C7C2×C3×C47
LCSG ▷ C3×C7
UCSC1 ◁ C2×C47

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 39);