Finite Group Databasebeta

← Prev (#37528285) Next (#37528287) →

C11×C3⋊(C7⋊#1035) #37528286

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

Aliases

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

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C4
derived, HallC3×C7×C25 ⋊ C4×C11
HallC7×C11×C25 ⋊ Dic3
HallC3×C11×C25 ⋊ Dic7
HallC11×C25 ⋊ Dic21
HallC3×C7×C11 ⋊ #1035
HallC7×C25 ⋊ C11×Dic3
HallC7×C11 ⋊ C3⋊#1035
HallC3×C25 ⋊ C11×Dic7
HallC3×C11 ⋊ C7⋊#1035
SylowC25 ⋊ C11×Dic21
HallC3×C7 ⋊ C11×#1035
SylowC7 ⋊ C11×C3⋊#1035
SylowC3 ⋊ C11×C7⋊#1035

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C7⋊#1035)
commutator, hypocenterC3×C7×C25C4×C11
FrattiniC5C11×C3⋊(C7⋊AGL(1,𝔽5))
FittingC3×C7×C11×C25C4
socleC3×C5×C7×C11AGL(1,𝔽5)
prime radicalC3×C7×C11×D25C2
cosocleC3×C7×D25C2×C11
LCSG ▷ C3×C7×C25
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 97);