Finite Group Databasebeta

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C7×C9×C11×AGL(1,𝔽5) #28357412

order13860
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C11×AGL(1,𝔽5)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C9×C11
HallC5×C9×C11 ⋊ C4×C7
HallC5×C7×C11 ⋊ C4×C9
HallC5×C7×C9 ⋊ C4×C11
HallC5×C11 ⋊ C4×C7×C9
HallC5×C9 ⋊ C4×C7×C11
HallC5×C7 ⋊ C4×C9×C11

Subgroups

subgroupG/H
center, hypercenterC7×C9×C11AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C9×C11
FrattiniC3C3×C7×C11×AGL(1,𝔽5)
FittingC5×C7×C9×C11C4
socleC3×C5×C7×C11C3×C4
prime radicalC3×C7×D5×C11C2×C3
cosocleC3×D5C2×C3×C7×C11
LCSG ▷ C5
UCSC1 ◁ C7×C9×C11

72 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, 79);