Finite Group Databasebeta

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C32×C4×C127⋊C7 #44544726

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

Aliases

direct productC32×C4×C127⋊C7
unambiguous semidirect product(C32×C4×C127)⋊C7

Splittings

Fitting, HallC32×C4×C127 ⋊ C7
derived, SylowC127 ⋊ C32×C4×C7
HallC32×C127 ⋊ C4×C7
HallC4×C127 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC32×C4C127⋊C7
commutator, hypocenterC127C32×C4×C7
FrattiniC2C2×C32×C127⋊C7
FittingC32×C4×C127C7
socleC2×C32×C127C2×C7
prime radicalC2×C32×C127⋊C7C2
cosocleC2×C127C2×C32×C7
LCSG ▷ C127
UCSC1 ◁ C32×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4572

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 108);