Finite Group Databasebeta

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C4×C47×C43⋊C3 #37564632

order24252
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC4×C47×C43⋊C3
unambiguous semidirect product(C4×C43)⋊(C3×C47)
unambiguous semidirect product(C4×C43×C47)⋊C3

Splittings

Fitting, HallC4×C43×C47 ⋊ C3
derived, SylowC43 ⋊ C3×C4×C47
HallC43×C47 ⋊ C3×C4
HallC4×C43 ⋊ C3×C47

Subgroups

subgroupG/H
center, hypercenterC4×C47C43⋊C3
commutator, hypocenterC43C3×C4×C47
FrattiniC2C2×C47×C43⋊C3
FittingC4×C43×C47C3
socleC2×C43×C47C2×C3
prime radicalC2×C47×C43⋊C3C2
cosocleC2×C43C2×C3×C47
LCSG ▷ C43
UCSC1 ◁ C4×C47

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8084

Conjugacy classes & character table

3196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24252, 2);