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C2×C3×C13×C23⋊C11 #34089395

order19734
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C13 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC2×C3×C13×C23 ⋊ C11
derived, SylowC23 ⋊ C2×C3×C11×C13
HallC3×C13×C23 ⋊ C2×C11
HallC2×C13×C23 ⋊ C3×C11
HallC13×C23 ⋊ C2×C3×C11
HallC2×C3×C23 ⋊ C11×C13
HallC3×C23 ⋊ C2×C11×C13
HallC2×C23 ⋊ C3×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13C23⋊C11
commutator, cosocle, hypocenterC23C2×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C3×C13×C23C11
LCSG ▷ C23
UCSC1 ◁ C2×C3×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1794

Conjugacy classes & character table

1014 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 2);