Finite Group Databasebeta

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C5×C9×C53⋊C13 #44526514

order31005
automorphism?
homologyAbelianization (H1) = C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×C53⋊C13
unambiguous semidirect productC53⋊(C5×C9×C13)
unambiguous semidirect product(C5×C53)⋊(C9×C13)
unambiguous semidirect product(C9×C53)⋊(C5×C13)
unambiguous semidirect product(C5×C9×C53)⋊C13

Splittings

Fitting, HallC5×C9×C53 ⋊ C13
derived, SylowC53 ⋊ C5×C9×C13
HallC9×C53 ⋊ C5×C13
HallC5×C53 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC5×C9C53⋊C13
commutator, hypocenterC53C5×C9×C13
FrattiniC3C3×C5×C53⋊C13
FittingC5×C9×C53C13
socleC3×C5×C53C3×C13
prime radicalC3×C5×C53⋊C13C3
cosocleC3×C53C3×C5×C13
LCSG ▷ C53
UCSC1 ◁ C5×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2385

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31005, 2);