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C7×C29×C9⋊AGL(1,𝔽5) #49141273

order36540
automorphism?
homologyAbelianization (H1) = C4×C7×C29 · Schur multiplier (H2) = C1

Aliases

direct productC7×C29×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(C7×AGL(1,𝔽5)×C29)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C4
derived, HallC5×C9 ⋊ C4×C7×C29
HallC7×C9×C29 ⋊ AGL(1,𝔽5)
HallC5×C9×C29 ⋊ C4×C7
HallC5×C7×C29 ⋊ Dic9
HallC5×C7×C9 ⋊ C4×C29
HallC9×C29 ⋊ C7×AGL(1,𝔽5)
HallC5×C29 ⋊ C7×Dic9
HallC7×C9 ⋊ AGL(1,𝔽5)×C29
HallC5×C7 ⋊ C29×Dic9
SylowC9 ⋊ C7×AGL(1,𝔽5)×C29
SylowC5 ⋊ C7×C29×Dic9

Subgroups

subgroupG/H
center, hypercenterC7×C29C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C7×C29
FrattiniC3C7×C29×ΓL(1,𝔽16)
FittingC5×C7×C9×C29C4
socleC3×C5×C7×C29Dic3
prime radicalC3×C7×D5×C29D3
cosocleC9×D5C2×C7×C29
LCSG ▷ C5×C9
UCSC1 ◁ C7×C29

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4263 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 115);