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C22⋊(#13183715⋊C5) #47977628

order35340
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC22⋊(#13183715⋊C5)
unambiguous semidirect product(C22⋊#13183715)⋊C5

Splittings

Fitting, socle, derived, HallC22×C19×C31 ⋊ C3×C5
HallC22×C19×ΓL(1,𝔽32) ⋊ C3
HallC22⋊#13183715 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ A4
HallC22×ΓL(1,𝔽32) ⋊ C19⋊C3
HallC19×C31 ⋊ C5×A4
HallΓL(1,𝔽32) ⋊ C22⋊(C19⋊C3)
HallC22×C31 ⋊ C5×C19⋊C3
HallC22×C19 ⋊ (C31⋊C3)⋊C5
SylowC31 ⋊ C5×C22⋊(C19⋊C3)
SylowC19 ⋊ C22⋊((C31⋊C3)⋊C5)
SylowC22 ⋊ #13183715⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C19×C31C3×C5
LCSG ▷ C22×C19×C31
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2356

Polycyclic presentation:

3,5,2^2,19,31|c^a=d,d^a=cd,e^a=e^7,f^a=f^25,f^b=f^16

Conjugacy classes & character table

292 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 100);