Finite Group Databasebeta

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C7×C3⋊(C11⋊#1035) #37528285

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

Aliases

direct productC7×C3⋊(C11⋊#1035)
unambiguous semidirect productC3⋊(C7×C11⋊#1035)
unambiguous semidirect productC11⋊(C7×C3⋊#1035)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C4
derived, HallC3×C11×C25 ⋊ C4×C7
HallC7×C11×C25 ⋊ Dic3
HallC3×C7×C25 ⋊ Dic11
HallC11×C25 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ #1035
HallC7×C25 ⋊ Dic33
HallC7×C11 ⋊ C3⋊#1035
HallC3×C25 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×#1035
SylowC25 ⋊ C7×Dic33
HallC3×C7 ⋊ C11⋊#1035
SylowC11 ⋊ C7×C3⋊#1035
SylowC3 ⋊ C7×C11⋊#1035

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C11⋊#1035)
commutator, hypocenterC3×C11×C25C4×C7
FrattiniC5C7×C3⋊(C11⋊AGL(1,𝔽5))
FittingC3×C7×C11×C25C4
socleC3×C5×C7×C11AGL(1,𝔽5)
prime radicalC3×C7×C11×D25C2
cosocleC3×C11×D25C2×C7
LCSG ▷ C3×C11×C25
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 96);