Finite Group Databasebeta

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Dic3×C13⋊C3×C73 #46802772

order34164
automorphism?
homologyAbelianization (H1) = C3×C4×C73 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C13⋊C3×C73
unambiguous semidirect productC3⋊(C4×C13⋊C3×C73)
unambiguous semidirect product(Dic3×C13)⋊(C3×C73)

Splittings

derivedC3×C13 ⋊ C3×C4×C73
HallC3×C13⋊C3×C73 ⋊ C4
HallC13×C73 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C73
SylowC13 ⋊ C3×Dic3×C73

Subgroups

subgroupG/H
center, hypercenterC2×C73D3×C13⋊C3
commutator, hypocenterC3×C13C3×C4×C73
FrattiniC2D3×C13⋊C3×C73
Fitting, socleC2×C3×C13×C73C2×C3
prime radicalC2×C3×C13⋊C3×C73C2
cosocleC2×C3×C13C2×C3×C73
LCSG ▷ C3×C13
UCSC1 ◁ C2×C73

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11388

Conjugacy classes & character table

3066 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34164, 138);