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C3×(C31⋊C3)⋊Dic31 #46829348

order34596
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C31⋊C3)⋊Dic31
unambiguous semidirect product(C31⋊C3)⋊(C3×Dic31)

Splittings

derived, SylowC312 ⋊ C32×C4
HallC3×C31×C31⋊C3 ⋊ C4
HallC31⋊Dic31 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3(C31⋊C3)⋊D31
commutator, hypocenterC312C32×C4
FrattiniC2C3×(C31⋊C3)⋊D31
Fitting, socleC2×C3×C312C2×C3
prime radicalC2×C3×C31×C31⋊C3C2
cosocleC2×C312C2×C32
LCSG ▷ C312
UCSC1 ◁ C2×C3

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1116

Conjugacy classes & character table

1236 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 108);