Finite Group Databasebeta

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C3×C4×(C127⋊C3)⋊C7 #44544704

order32004
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×(C127⋊C3)⋊C7
unambiguous semidirect product(C4×C127⋊C3)⋊(C3×C7)
unambiguous semidirect product(C4×C127⋊C7)⋊C32
unambiguous semidirect product(C3×C4×C127⋊C3)⋊C7
unambiguous semidirect product(C3×C4×C127⋊C7)⋊C3

Splittings

FittingC3×C4×C127 ⋊ C3×C7
derived, SylowC127 ⋊ C32×C4×C7
HallC3×C4×C127⋊C3 ⋊ C7
HallC4×C127⋊C7 ⋊ C32
HallC3×C127⋊C3 ⋊ C4×C7
HallC127⋊C7 ⋊ C32×C4
HallC4×C127 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4(C127⋊C3)⋊C7
commutator, hypocenterC127C32×C4×C7
FrattiniC2C2×C3×(C127⋊C3)⋊C7
FittingC3×C4×C127C3×C7
socleC2×C3×C127C2×C3×C7
prime radicalC2×C3×(C127⋊C3)⋊C7C2
cosocleC2×C127C2×C32×C7
LCSG ▷ C127
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1524

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 86);