Finite Group Databasebeta

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C3×C4×C13⋊C3×C79 #49149489

order36972
automorphism?
homologyAbelianization (H1) = C32×C4×C79 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C13⋊C3×C79
unambiguous semidirect product(C4×C13)⋊(C32×C79)
unambiguous semidirect product(C3×C4×C13)⋊(C3×C79)

Splittings

FittingC3×C4×C13×C79 ⋊ C3
derived, SylowC13 ⋊ C32×C4×C79
HallC4×C13×C79 ⋊ C32
HallC13×C79 ⋊ C32×C4
HallC4×C13 ⋊ C32×C79

Subgroups

subgroupG/H
center, hypercenterC3×C4×C79C13⋊C3
commutator, hypocenterC13C32×C4×C79
FrattiniC2C2×C3×C13⋊C3×C79
FittingC3×C4×C13×C79C3
socleC2×C3×C13×C79C2×C3
prime radicalC2×C3×C13⋊C3×C79C2
cosocleC2×C13C2×C32×C79
LCSG ▷ C13
UCSC1 ◁ C3×C4×C79

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12324

Conjugacy classes & character table

6636 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 137);