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C13×C3⋊AGL(1,𝔽29) #44539784

order31668
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊AGL(1,𝔽29)
unambiguous semidirect productC3⋊(C13×AGL(1,𝔽29))
unambiguous semidirect product(C3⋊#1181)⋊(C7×C13)
unambiguous semidirect product(C13×C3⋊#1181)⋊C7

Splittings

Fitting, socle, HallC3×C13×C29 ⋊ C4×C7
derived, HallC3×C29 ⋊ C4×C7×C13
HallC3×C13×C29⋊C7 ⋊ C4
HallC13×C3⋊#1181 ⋊ C7
HallC13×C29⋊C7 ⋊ Dic3
HallC3×C29⋊C7 ⋊ C4×C13
HallC13×C29 ⋊ C7×Dic3
HallC3⋊#1181 ⋊ C7×C13
HallC29⋊C7 ⋊ Dic3×C13
HallC3×C13 ⋊ AGL(1,𝔽29)
SylowC29 ⋊ C7×Dic3×C13
SylowC3 ⋊ C13×AGL(1,𝔽29)

Subgroups

subgroupG/H
center, hypercenterC13C3⋊AGL(1,𝔽29)
commutator, hypocenterC3×C29C4×C7×C13
FrattiniC1G
Fitting, socleC3×C13×C29C4×C7
prime radicalC3×C13×D29⋊C7C2
cosocleC3×D29C2×C7×C13
LCSG ▷ C3×C29
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1131

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 79);