Finite Group Databasebeta

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C3×C4×C7×C127⋊C3 #44544758

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

Aliases

direct productC3×C4×C7×C127⋊C3

Splittings

FittingC3×C4×C7×C127 ⋊ C3
derived, SylowC127 ⋊ C32×C4×C7
HallC4×C7×C127 ⋊ C32
HallC7×C127 ⋊ C32×C4
HallC4×C127 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4×C7C127⋊C3
commutator, hypocenterC127C32×C4×C7
FrattiniC2C2×C3×C7×C127⋊C3
FittingC3×C4×C7×C127C3
socleC2×C3×C7×C127C2×C3
prime radicalC2×C3×C7×C127⋊C3C2
cosocleC2×C127C2×C32×C7
LCSG ▷ C127
UCSC1 ◁ C3×C4×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10668

Conjugacy classes & character table

3780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 140);