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C32×C7⋊(C11⋊AGL(1,𝔽5)) #28357653

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

Aliases

direct productC32×C7⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C32×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C4
derived, HallC5×C7×C11 ⋊ C32×C4
HallC32×C7×C11 ⋊ AGL(1,𝔽5)
HallC32×C5×C11 ⋊ Dic7
HallC32×C5×C7 ⋊ Dic11
HallC32×C11 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C11 ⋊ C32×AGL(1,𝔽5)
HallC32×C7 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ C32×Dic7
HallC32×C5 ⋊ Dic77
HallC5×C7 ⋊ C32×Dic11
SylowC11 ⋊ C32×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C32×C11⋊AGL(1,𝔽5)
SylowC5 ⋊ C32×Dic77

Subgroups

subgroupG/H
center, hypercenterC32C7⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C11C32×C4
FrattiniC1G
Fitting, socleC32×C5×C7×C11C4
prime radicalC32×C7×D5×C11C2
cosocleC7×D5×C11C2×C32
LCSG ▷ C5×C7×C11
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

1413 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 320);