Finite Group Databasebeta

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C4×#13183714⋊C5 #47977538

order35340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×#13183714⋊C5
unambiguous semidirect product(C4×#13183714)⋊C5

Splittings

Fitting, HallC4×C19×C31 ⋊ C3×C5
derived, HallC19×C31 ⋊ C3×C4×C5
HallC4×C19×ΓL(1,𝔽32) ⋊ C3
HallC4×#13183714 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C3×C4
Hall#13183714 ⋊ C4×C5
HallC4×ΓL(1,𝔽32) ⋊ C19⋊C3
HallΓL(1,𝔽32) ⋊ C4×C19⋊C3
HallC4×C31 ⋊ C5×C19⋊C3
HallC4×C19 ⋊ (C31⋊C3)⋊C5
SylowC31 ⋊ C4×C5×C19⋊C3
SylowC19 ⋊ C4×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC4#13183714⋊C5
commutator, hypocenterC19×C31C3×C4×C5
FrattiniC2C2×#13183714⋊C5
FittingC4×C19×C31C3×C5
socle, cosocleC2×C19×C31C2×C3×C5
prime radicalC2×#13183714⋊C5C2
LCSG ▷ C19×C31
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2356

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 10);