Finite Group Databasebeta

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C3×Dic3×C13×C73 #46802791

order34164
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C73 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derivedC3 ⋊ C3×C4×C13×C73
HallC32×C13×C73 ⋊ C4
HallC32×C73 ⋊ C4×C13
HallC32×C13 ⋊ C4×C73
SylowC32 ⋊ C4×C13×C73

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13×C73D3
commutator, hypocenterC3C3×C4×C13×C73
FrattiniC2C3×D3×C13×C73
Fitting, socle, prime radicalC2×C32×C13×C73C2
cosocleC2×C3C2×C3×C13×C73
LCSG ▷ C3
UCSC1 ◁ C2×C3×C13×C73

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11388

Conjugacy classes & character table

17082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34164, 157);