Finite Group Databasebeta

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C3×C3⋊(Dic113⋊C7) #43249804

order28476
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(Dic113⋊C7)
unambiguous semidirect productC3⋊(C3×Dic113⋊C7)
unambiguous semidirect productDic339⋊(C3×C7)
unambiguous semidirect product(C3×Dic339)⋊C7

Splittings

derivedC3×C113 ⋊ C3×C4×C7
HallC32×C113⋊C7 ⋊ C4
HallC3×Dic339 ⋊ C7
HallC32×C113 ⋊ C4×C7
HallC113⋊C7 ⋊ C3×Dic3
SylowC113 ⋊ C3×C7×Dic3
SylowC32 ⋊ Dic113⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D113⋊C7)
commutator, hypocenterC3×C113C3×C4×C7
FrattiniC2C3×C3⋊(D113⋊C7)
Fitting, socleC2×C32×C113C2×C7
prime radicalC2×C32×C113⋊C7C2
cosocleC2×C3×C113C2×C3×C7
LCSG ▷ C3×C113
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1356

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28476, 55);