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C11×C23⋊(D13⋊C3) #34089422

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

Aliases

direct productC11×C23⋊(D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C11×D23)
unambiguous semidirect product(C11×D299)⋊C3

Splittings

Fitting, socle, HallC11×C13×C23 ⋊ C2×C3
derived, HallC13×C23 ⋊ C2×C3×C11
HallC11×C23×C13⋊C3 ⋊ C2
HallC11×D299 ⋊ C3
HallC23×C13⋊C3 ⋊ C2×C11
HallD299 ⋊ C3×C11
HallC11×C13⋊C3 ⋊ D23
HallC11×C23 ⋊ D13⋊C3
HallC11×C13 ⋊ C3×D23
HallC13⋊C3 ⋊ C11×D23
SylowC23 ⋊ C11×D13⋊C3
SylowC13 ⋊ C3×C11×D23

Subgroups

subgroupG/H
center, hypercenterC11C23⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C23C2×C3×C11
FrattiniC1G
Fitting, socleC11×C13×C23C2×C3
LCSG ▷ C13×C23
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3289

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 29);