Finite Group Databasebeta

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D3×C11×C13×C23 #34089405

order19734
automorphism?
homologyAbelianization (H1) = C2×C11×C13×C23 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11×C13×C23
unambiguous semidirect productC3⋊(C2×C11×C13×C23)

Splittings

Fitting, socle, HallC3×C11×C13×C23 ⋊ C2
derived, SylowC3 ⋊ C2×C11×C13×C23
HallC3×C13×C23 ⋊ C2×C11
HallC3×C11×C23 ⋊ C2×C13
HallC3×C11×C13 ⋊ C2×C23
HallC3×C23 ⋊ C2×C11×C13
HallC3×C13 ⋊ C2×C11×C23
HallC3×C11 ⋊ C2×C13×C23

Subgroups

subgroupG/H
center, hypercenterC11×C13×C23D3
commutator, cosocle, hypocenterC3C2×C11×C13×C23
FrattiniC1G
Fitting, socleC3×C11×C13×C23C2
LCSG ▷ C3
UCSC1 ◁ C11×C13×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9867

Conjugacy classes & character table

9867 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 12);