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C13×(C7⋊C9)⋊AGL(1,𝔽5) #30655016

order16380
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C7⋊C9)⋊AGL(1,𝔽5)
unambiguous semidirect product(C7⋊C9)⋊(C13×AGL(1,𝔽5))
unambiguous semidirect product(C7⋊AGL(1,𝔽5))⋊(C9×C13)

Splittings

derived, HallC5×C7 ⋊ C4×C9×C13
HallC5×C13×C7⋊C9 ⋊ C4
HallC13×C7⋊AGL(1,𝔽5) ⋊ C9
HallC13×C7⋊C9 ⋊ AGL(1,𝔽5)
HallC5×C7×C13 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C13
HallC7⋊AGL(1,𝔽5) ⋊ C9×C13
HallC7×C13 ⋊ C9×AGL(1,𝔽5)
HallC5×C13 ⋊ Dic7⋊C9
HallC7⋊C9 ⋊ C13×AGL(1,𝔽5)
SylowC7 ⋊ C9×C13×AGL(1,𝔽5)
SylowC5 ⋊ C13×Dic7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C9×C13
FrattiniC3C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C7×D5×C13C2×C3
cosocleC3×C7×D5C2×C3×C13
LCSG ▷ C5×C7
UCSC1 ◁ C3×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 66);