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C32×C7⋊(Dic11⋊C5) #28357482

order13860
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C32×Dic7)
unambiguous semidirect product(C32×Dic77)⋊C5

Splittings

derived, HallC7×C11 ⋊ C32×C4×C5
HallC32×C7×C11⋊C5 ⋊ C4
HallC32×Dic77 ⋊ C5
HallC32×C7×C11 ⋊ C4×C5
HallC32×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ C32×C4
HallDic77 ⋊ C32×C5
HallC32×C11 ⋊ C5×Dic7
HallC32×C7 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C32×Dic7
SylowC11 ⋊ C32×C5×Dic7
SylowC7 ⋊ C32×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C32C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C32×C4×C5
FrattiniC2C32×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C32×C7×C11C2×C5
prime radicalC2×C32×C7×C11⋊C5C2
cosocleC2×C7×C11C2×C32×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 149);