Finite Group Databasebeta

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C32×Dic131⋊C5 #37556065

order23580
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×Dic131⋊C5
unambiguous semidirect productDic131⋊(C32×C5)
unambiguous semidirect product(C131⋊C5)⋊(C32×C4)
unambiguous semidirect product(C3×Dic131)⋊(C3×C5)
unambiguous semidirect product(C32×Dic131)⋊C5

Splittings

derived, SylowC131 ⋊ C32×C4×C5
HallC32×C131⋊C5 ⋊ C4
HallC32×Dic131 ⋊ C5
HallC32×C131 ⋊ C4×C5
HallC131⋊C5 ⋊ C32×C4
HallDic131 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32D131⋊C5
commutator, hypocenterC131C32×C4×C5
FrattiniC2C32×D131⋊C5
Fitting, socleC2×C32×C131C2×C5
prime radicalC2×C32×C131⋊C5C2
cosocleC2×C131C2×C32×C5
LCSG ▷ C131
UCSC1 ◁ C2×C32

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4716

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, 40);