Finite Group Databasebeta

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C31×C3⋊(C19⋊AGL(1,𝔽5)) #47977733

order35340
automorphism?
homologyAbelianization (H1) = C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×C3⋊(C19⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C31×C19⋊AGL(1,𝔽5))
unambiguous semidirect productC19⋊(C31×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C19×C31 ⋊ C4
derived, HallC3×C5×C19 ⋊ C4×C31
HallC5×C19×C31 ⋊ Dic3
HallC3×C19×C31 ⋊ AGL(1,𝔽5)
HallC19×C31 ⋊ ΓL(1,𝔽16)
HallC3×C5×C31 ⋊ Dic19
HallC5×C31 ⋊ Dic57
HallC5×C19 ⋊ Dic3×C31
HallC3×C31 ⋊ C19⋊AGL(1,𝔽5)
HallC3×C19 ⋊ AGL(1,𝔽5)×C31
SylowC19 ⋊ C31×ΓL(1,𝔽16)
HallC3×C5 ⋊ C31×Dic19
SylowC5 ⋊ C31×Dic57
SylowC3 ⋊ C31×C19⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC31C3⋊(C19⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C19C4×C31
FrattiniC1G
Fitting, socleC3×C5×C19×C31C4
prime radicalC3×D5×C19×C31C2
cosocleC3×D5×C19C2×C31
LCSG ▷ C3×C5×C19
UCSC1 ◁ C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8835

Conjugacy classes & character table

3627 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 205);