Finite Group Databasebeta

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C32×C5×C53⋊C13 #44526517

order31005
automorphism?
homologyAbelianization (H1) = C32×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C53⋊C13
unambiguous semidirect productC53⋊(C32×C5×C13)
unambiguous semidirect product(C3×C53)⋊(C3×C5×C13)
unambiguous semidirect product(C5×C53)⋊(C32×C13)
unambiguous semidirect product(C32×C53)⋊(C5×C13)
unambiguous semidirect product(C3×C5×C53)⋊(C3×C13)
unambiguous semidirect product(C32×C5×C53)⋊C13

Splittings

Fitting, socle, HallC32×C5×C53 ⋊ C13
derived, SylowC53 ⋊ C32×C5×C13
HallC32×C53 ⋊ C5×C13
HallC5×C53 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC32×C5C53⋊C13
commutator, cosocle, hypocenterC53C32×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C53C13
LCSG ▷ C53
UCSC1 ◁ C32×C5

48 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, 5);