Finite Group Databasebeta

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C2×C32×D131⋊C5 #37556091

order23580
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D131⋊C5
unambiguous semidirect productD131⋊(C2×C32×C5)
unambiguous semidirect product(C2×D131)⋊(C32×C5)
unambiguous semidirect product(C131⋊C5)⋊(C22×C32)
unambiguous semidirect product(C2×C131⋊C5)⋊(C2×C32)
unambiguous semidirect product(C2×C3×D131)⋊(C3×C5)
unambiguous semidirect product(C2×C32×D131)⋊C5

Splittings

Fitting, socleC2×C32×C131 ⋊ C2×C5
derived, SylowC131 ⋊ C22×C32×C5
HallC32×C131⋊C5 ⋊ C22
HallC2×C32×D131 ⋊ C5
HallC32×C131 ⋊ C22×C5
HallC131⋊C5 ⋊ C22×C32
HallC2×D131 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32D131⋊C5
commutator, cosocle, hypocenterC131C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C131C2×C5
LCSG ▷ C131
UCSC1 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2358

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 66);