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C3×C13×AGL(1,𝔽5)×ΓL(1,𝔽8) #30655338

order16380
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13×AGL(1,𝔽5)×ΓL(1,𝔽8)
unambiguous semidirect product(C7×AGL(1,𝔽5))⋊(C32×C13)
unambiguous semidirect product(C3×C7×AGL(1,𝔽5))⋊(C3×C13)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derived, HallC5×C7 ⋊ C32×C4×C13
HallC3×C5×C13×ΓL(1,𝔽8) ⋊ C4
HallC7×C13×AGL(1,𝔽5) ⋊ C32
HallC5×C7×C13 ⋊ C32×C4
HallC3×C5×ΓL(1,𝔽8) ⋊ C4×C13
HallC7×AGL(1,𝔽5) ⋊ C32×C13
HallC7×C13 ⋊ C32×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×C4×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C13×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×C13×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C13AGL(1,𝔽5)×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C32×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×D5×C13×ΓL(1,𝔽8)C2
cosocleC7×D5C2×C32×C13
LCSG ▷ C5×C7
UCSC1 ◁ C3×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 388);