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C7×C13×C9⋊AGL(1,𝔽5) #30655131

order16380
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(C7×C13×AGL(1,𝔽5))

Splittings

Fitting, HallC5×C7×C9×C13 ⋊ C4
derived, HallC5×C9 ⋊ C4×C7×C13
HallC7×C9×C13 ⋊ AGL(1,𝔽5)
HallC5×C9×C13 ⋊ C4×C7
HallC5×C7×C13 ⋊ Dic9
HallC5×C7×C9 ⋊ C4×C13
HallC9×C13 ⋊ C7×AGL(1,𝔽5)
HallC5×C13 ⋊ C7×Dic9
HallC7×C9 ⋊ C13×AGL(1,𝔽5)
HallC5×C7 ⋊ C13×Dic9
SylowC9 ⋊ C7×C13×AGL(1,𝔽5)
SylowC5 ⋊ C7×C13×Dic9

Subgroups

subgroupG/H
center, hypercenterC7×C13C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C7×C13
FrattiniC3C7×C13×ΓL(1,𝔽16)
FittingC5×C7×C9×C13C4
socleC3×C5×C7×C13Dic3
prime radicalC3×C7×D5×C13D3
cosocleC9×D5C2×C7×C13
LCSG ▷ C5×C9
UCSC1 ◁ C7×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

1911 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 181);