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C3×C47×C23⋊C11 #49087367

order35673
automorphism?
homologyAbelianization (H1) = C3×C11×C47 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47×C23⋊C11
unambiguous semidirect productC23⋊(C3×C11×C47)
unambiguous semidirect product(C3×C23)⋊(C11×C47)
unambiguous semidirect product(C23×C47)⋊(C3×C11)
unambiguous semidirect product(C3×C23×C47)⋊C11

Splittings

Fitting, socle, HallC3×C23×C47 ⋊ C11
derived, SylowC23 ⋊ C3×C11×C47
HallC23×C47 ⋊ C3×C11
HallC3×C23 ⋊ C11×C47

Subgroups

subgroupG/H
center, hypercenterC3×C47C23⋊C11
commutator, cosocle, hypocenterC23C3×C11×C47
FrattiniC1G
Fitting, socleC3×C23×C47C11
LCSG ▷ C23
UCSC1 ◁ C3×C47

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3243

Conjugacy classes & character table

1833 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35673, 3);