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C2×C13⋊C3×C23⋊C11 #34089397

order19734
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C13⋊C3×C23⋊C11
unambiguous semidirect product(C2×C13)⋊(C3×C23⋊C11)
unambiguous semidirect product(C2×C23)⋊(C11×C13⋊C3)
unambiguous semidirect product(C2×C23×C13⋊C3)⋊C11
unambiguous semidirect product(C2×C13×C23⋊C11)⋊C3

Splittings

Fitting, socle, HallC2×C13×C23 ⋊ C3×C11
derived, HallC13×C23 ⋊ C2×C3×C11
HallC2×C13×C23⋊C11 ⋊ C3
HallC13×C23⋊C11 ⋊ C2×C3
HallC2×C23×C13⋊C3 ⋊ C11
HallC23×C13⋊C3 ⋊ C2×C11
HallC2×C23 ⋊ C11×C13⋊C3
HallC2×C13 ⋊ C3×C23⋊C11
SylowC23 ⋊ C2×C11×C13⋊C3
SylowC13 ⋊ C2×C3×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×C23⋊C11
commutator, cosocle, hypocenterC13×C23C2×C3×C11
FrattiniC1G
Fitting, socleC2×C13×C23C3×C11
LCSG ▷ C13×C23
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 598

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 4);