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C29×C7⋊(C9⋊AGL(1,𝔽5)) #49141277

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

Aliases

direct productC29×C7⋊(C9⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C29×C9⋊AGL(1,𝔽5))
unambiguous semidirect productC9⋊(C29×C7⋊AGL(1,𝔽5))

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C4
derived, HallC5×C7×C9 ⋊ C4×C29
HallC7×C9×C29 ⋊ AGL(1,𝔽5)
HallC5×C9×C29 ⋊ Dic7
HallC5×C7×C29 ⋊ Dic9
HallC9×C29 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C29 ⋊ C9⋊AGL(1,𝔽5)
HallC5×C29 ⋊ Dic63
HallC7×C9 ⋊ AGL(1,𝔽5)×C29
HallC5×C9 ⋊ Dic7×C29
HallC5×C7 ⋊ C29×Dic9
SylowC9 ⋊ C29×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C29×C9⋊AGL(1,𝔽5)
SylowC5 ⋊ C29×Dic63

Subgroups

subgroupG/H
center, hypercenterC29C7⋊(C9⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C9C4×C29
FrattiniC3C29×C3⋊(C7⋊AGL(1,𝔽5))
FittingC5×C7×C9×C29C4
socleC3×C5×C7×C29Dic3
prime radicalC3×C7×D5×C29D3
cosocleC7×C9×D5C2×C29
LCSG ▷ C5×C7×C9
UCSC1 ◁ C29

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

3741 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 119);