Finite Group Databasebeta

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C3×C11⋊(Dic73⋊C3) #43274847

order28908
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11⋊(Dic73⋊C3)
unambiguous semidirect productC11⋊(C3×Dic73⋊C3)
unambiguous semidirect productDic803⋊C32
unambiguous semidirect product(C3×Dic803)⋊C3

Splittings

derived, HallC11×C73 ⋊ C32×C4
HallC3×C11×C73⋊C3 ⋊ C4
HallDic803 ⋊ C32
HallC3×C73⋊C3 ⋊ Dic11
SylowC73 ⋊ C32×Dic11
SylowC11 ⋊ C3×Dic73⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊(D73⋊C3)
commutator, hypocenterC11×C73C32×C4
FrattiniC2C3×C11⋊(D73⋊C3)
Fitting, socleC2×C3×C11×C73C2×C3
prime radicalC2×C3×C11×C73⋊C3C2
cosocleC2×C11×C73C2×C32
LCSG ▷ C11×C73
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9636

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28908, 47);