Finite Group Databasebeta

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C5×C59×C37⋊C3 #45658688

order32745
automorphism?
homologyAbelianization (H1) = C3×C5×C59 · Schur multiplier (H2) = C1

Aliases

direct productC5×C59×C37⋊C3
unambiguous semidirect productC37⋊(C3×C5×C59)
unambiguous semidirect product(C5×C37)⋊(C3×C59)
unambiguous semidirect product(C37×C59)⋊(C3×C5)
unambiguous semidirect product(C5×C37×C59)⋊C3

Splittings

Fitting, socle, HallC5×C37×C59 ⋊ C3
derived, SylowC37 ⋊ C3×C5×C59
HallC37×C59 ⋊ C3×C5
HallC5×C37 ⋊ C3×C59

Subgroups

subgroupG/H
center, hypercenterC5×C59C37⋊C3
commutator, cosocle, hypocenterC37C3×C5×C59
FrattiniC1G
Fitting, socleC5×C37×C59C3
LCSG ▷ C37
UCSC1 ◁ C5×C59

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10915

Conjugacy classes & character table

4425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32745, 2);