Finite Group Databasebeta

← Prev (#44544738) Next (#44544740) →

C7×C3⋊((C127⋊C3)⋊C4) #44544739

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

Aliases

direct productC7×C3⋊((C127⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C7×(C127⋊C3)⋊C4)

Splittings

derivedC3×C127 ⋊ C3×C4×C7
HallC3×C7×C127⋊C3 ⋊ C4
HallC3×C127⋊C3 ⋊ C4×C7
HallC7×C127 ⋊ C3×Dic3
SylowC127 ⋊ C3×C7×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(D127⋊C3)
commutator, hypocenterC3×C127C3×C4×C7
FrattiniC2C7×C3⋊(D127⋊C3)
Fitting, socleC2×C3×C7×C127C2×C3
prime radicalC2×C3×C7×C127⋊C3C2
cosocleC2×C3×C127C2×C3×C7
LCSG ▷ C3×C127
UCSC1 ◁ C2×C7

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10668

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 121);