Finite Group Databasebeta

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C5×C19⋊C3×C113 #44567224

order32205
automorphism?
homologyAbelianization (H1) = C3×C5×C113 · Schur multiplier (H2) = C1

Aliases

direct productC5×C19⋊C3×C113
unambiguous semidirect productC19⋊(C3×C5×C113)
unambiguous semidirect product(C5×C19)⋊(C3×C113)
unambiguous semidirect product(C19×C113)⋊(C3×C5)
unambiguous semidirect product(C5×C19×C113)⋊C3

Splittings

Fitting, socle, HallC5×C19×C113 ⋊ C3
derived, SylowC19 ⋊ C3×C5×C113
HallC19×C113 ⋊ C3×C5
HallC5×C19 ⋊ C3×C113

Subgroups

subgroupG/H
center, hypercenterC5×C113C19⋊C3
commutator, cosocle, hypocenterC19C3×C5×C113
FrattiniC1G
Fitting, socleC5×C19×C113C3
LCSG ▷ C19
UCSC1 ◁ C5×C113

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10735

Conjugacy classes & character table

5085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32205, 2);