Finite Group Databasebeta

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C7×C11×C3⋊#1035 #37528284

order23100
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×C3⋊#1035
unambiguous semidirect productC3⋊(C7×C11×#1035)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C4
derived, HallC3×C25 ⋊ C4×C7×C11
HallC7×C11×C25 ⋊ Dic3
HallC3×C11×C25 ⋊ C4×C7
HallC3×C7×C25 ⋊ C4×C11
HallC11×C25 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ #1035
HallC7×C25 ⋊ C11×Dic3
HallC3×C11 ⋊ C7×#1035
SylowC25 ⋊ C7×C11×Dic3
HallC3×C7 ⋊ C11×#1035
SylowC3 ⋊ C7×C11×#1035

Subgroups

subgroupG/H
center, hypercenterC7×C11C3⋊#1035
commutator, hypocenterC3×C25C4×C7×C11
FrattiniC5C7×C11×ΓL(1,𝔽16)
FittingC3×C7×C11×C25C4
socleC3×C5×C7×C11AGL(1,𝔽5)
prime radicalC3×C7×C11×D25C2
cosocleC3×D25C2×C7×C11
LCSG ▷ C3×C25
UCSC1 ◁ C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 95);