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C7×AGL(1,𝔽5)×C13⋊C9 #30655015

order16380
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, HallC5×C13 ⋊ C4×C7×C9
HallC5×C7×C13⋊C9 ⋊ C4
HallC7×C13×AGL(1,𝔽5) ⋊ C9
HallC5×C13⋊C9 ⋊ C4×C7
HallC5×C7×C13 ⋊ C4×C9
HallC13×AGL(1,𝔽5) ⋊ C7×C9
HallC7×C13 ⋊ C9×AGL(1,𝔽5)
HallC5×C7 ⋊ C4×C13⋊C9
SylowC13 ⋊ C7×C9×AGL(1,𝔽5)
SylowC5 ⋊ C4×C7×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C7AGL(1,𝔽5)×C13⋊C3
commutator, hypocenterC5×C13C4×C7×C9
FrattiniC3C7×AGL(1,𝔽5)×C13⋊C3
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C7×D5×C13C2×C3
cosocleC3×D5×C13C2×C3×C7
LCSG ▷ C5×C13
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 65);