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C29×C3⋊((C31⋊C3)⋊C4) #44569059

order32364
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×C3⋊((C31⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C29×(C31⋊C3)⋊C4)
unambiguous semidirect product(C31⋊C3)⋊(Dic3×C29)
unambiguous semidirect productDic93⋊(C3×C29)
unambiguous semidirect product(C29×Dic93)⋊C3

Splittings

derivedC3×C31 ⋊ C3×C4×C29
HallC3×C29×C31⋊C3 ⋊ C4
HallC29×C31 ⋊ C3×Dic3
HallC3×C31⋊C3 ⋊ C4×C29
SylowC31 ⋊ C3×Dic3×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29C3⋊(D31⋊C3)
commutator, hypocenterC3×C31C3×C4×C29
FrattiniC2C29×C3⋊(D31⋊C3)
Fitting, socleC2×C3×C29×C31C2×C3
prime radicalC2×C3×C29×C31⋊C3C2
cosocleC2×C3×C31C2×C3×C29
LCSG ▷ C3×C31
UCSC1 ◁ C2×C29

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10788

Conjugacy classes & character table

1392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 45);