Finite Group Databasebeta

← Prev (#28357480) Next (#28357482) →

C32×C7×Dic11⋊C5 #28357481

order13860
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×Dic11⋊C5
unambiguous semidirect productDic11⋊(C32×C5×C7)
unambiguous semidirect product(C11⋊C5)⋊(C32×C4×C7)
unambiguous semidirect product(C3×Dic11)⋊(C3×C5×C7)
unambiguous semidirect product(C32×Dic11)⋊(C5×C7)
unambiguous semidirect product(C32×C7×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C32×C4×C5×C7
HallC32×C7×C11⋊C5 ⋊ C4
HallC32×C7×Dic11 ⋊ C5
HallC32×C7×C11 ⋊ C4×C5
HallC32×C11⋊C5 ⋊ C4×C7
HallC32×Dic11 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ C32×C4
HallC7×Dic11 ⋊ C32×C5
HallC32×C11 ⋊ C4×C5×C7
HallC7×C11 ⋊ C32×C4×C5
HallC11⋊C5 ⋊ C32×C4×C7
HallDic11 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32×C7AGL(1,𝔽11)
commutator, hypocenterC11C32×C4×C5×C7
FrattiniC2C32×C7×AGL(1,𝔽11)
Fitting, socleC2×C32×C7×C11C2×C5
prime radicalC2×C32×C7×C11⋊C5C2
cosocleC2×C11C2×C32×C5×C7
LCSG ▷ C11
UCSC1 ◁ C2×C32×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 148);