Finite Group Databasebeta

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C32×C7×C11×AGL(1,𝔽5) #28357650

order13860
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C32×C4×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×C11×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C4
derived, SylowC5 ⋊ C32×C4×C7×C11
HallC32×C5×C11 ⋊ C4×C7
HallC5×C7×C11 ⋊ C32×C4
HallC32×C5×C7 ⋊ C4×C11
HallC5×C11 ⋊ C32×C4×C7
HallC32×C5 ⋊ C4×C7×C11
HallC5×C7 ⋊ C32×C4×C11

Subgroups

subgroupG/H
center, hypercenterC32×C7×C11AGL(1,𝔽5)
commutator, hypocenterC5C32×C4×C7×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C4
prime radicalC32×C7×D5×C11C2
cosocleD5C2×C32×C7×C11
LCSG ▷ C5
UCSC1 ◁ C32×C7×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 317);