Finite Group Databasebeta

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C11×C3⋊(C11⋊#1035) #49137178

order36300
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC3×C112×C25 ⋊ C4
derivedC3×C11×C25 ⋊ C4×C11
HallC112×C25 ⋊ Dic3
HallC3×C112 ⋊ #1035
SylowC112 ⋊ C3⋊#1035
HallC3×C25 ⋊ C11×Dic11
SylowC25 ⋊ C11×Dic33
SylowC3 ⋊ C11×C11⋊#1035

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C11⋊#1035)
commutator, hypocenterC3×C11×C25C4×C11
FrattiniC5C11×C3⋊(C11⋊AGL(1,𝔽5))
FittingC3×C112×C25C4
socleC3×C5×C112AGL(1,𝔽5)
prime radicalC3×C112×D25C2
cosocleC3×C11×D25C2×C11
LCSG ▷ C3×C11×C25
UCSC1 ◁ C11

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

2574 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 314);