Finite Group Databasebeta

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C3×C3⋊(Dic127⋊C7) #44544718

order32004
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(Dic127⋊C7)
unambiguous semidirect productC3⋊(C3×Dic127⋊C7)
unambiguous semidirect product(C3×Dic381)⋊C7

Splittings

derivedC3×C127 ⋊ C3×C4×C7
HallC32×C127⋊C7 ⋊ C4
HallC3×Dic381 ⋊ C7
HallC32×C127 ⋊ C4×C7
HallC127⋊C7 ⋊ C3×Dic3
SylowC127 ⋊ C3×C7×Dic3
SylowC32 ⋊ Dic127⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D127⋊C7)
commutator, hypocenterC3×C127C3×C4×C7
FrattiniC2C3×C3⋊(D127⋊C7)
Fitting, socleC2×C32×C127C2×C7
prime radicalC2×C32×C127⋊C7C2
cosocleC2×C3×C127C2×C3×C7
LCSG ▷ C3×C127
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1524

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 100);