Finite Group Databasebeta

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C3×C52×C22⋊(C13⋊C3) #26043862

order11700
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC3×C52×C22⋊(C13⋊C3)
unambiguous semidirect product(C22×C3)⋊(C52×C13⋊C3)
unambiguous semidirect product(C3×C13)⋊(C52×A4)
unambiguous semidirect product(C22×C3×C5)⋊(C5×C13⋊C3)
unambiguous semidirect product(C3×C5×C13)⋊(C5×A4)

Splittings

Fitting, socleC22×C3×C52×C13 ⋊ C3
derived, HallC22×C13 ⋊ C32×C52
HallC22×C52×C13 ⋊ C32
HallC52×C13 ⋊ C3×A4
HallC22×C52 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×C52×A4
SylowC22 ⋊ C3×C52×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C52C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C32×C52
FrattiniC1G
Fitting, socleC22×C3×C52×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C3×C52

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 709);