Finite Group Databasebeta

← Prev (#26043862) Next (#26043864) →

C3×C52×A4×C13 #26043863

order11700
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C52×C13 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC3×C52×A4×C13
unambiguous semidirect productC22⋊(C32×C52×C13)
unambiguous semidirect product(C22×C3)⋊(C3×C52×C13)
unambiguous semidirect product(C22×C5)⋊(C32×C5×C13)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C5×C13)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C52×C13A4
commutator, cosocle, hypocenterC22C32×C52×C13
FrattiniC1G
Fitting, socleC22×C3×C52×C13C3
LCSG ▷ C22
UCSC1 ◁ C3×C52×C13

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 710);