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C11×D885 #34085694

order19470
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D885
unambiguous semidirect productC3⋊(C11×D295)
unambiguous semidirect productC5⋊(C11×D177)
unambiguous semidirect productC59⋊(C11×D15)

Splittings

Fitting, socle, HallC3×C5×C11×C59 ⋊ C2
derived, HallC3×C5×C59 ⋊ C2×C11
HallC5×C11×C59 ⋊ D3
HallC3×C11×C59 ⋊ D5
HallC11×C59 ⋊ D15
HallC5×C59 ⋊ D3×C11
HallC3×C59 ⋊ D5×C11
HallC3×C5×C11 ⋊ D59
SylowC59 ⋊ C11×D15
HallC5×C11 ⋊ D177
HallC3×C11 ⋊ D295
HallC3×C5 ⋊ C11×D59
SylowC5 ⋊ C11×D177
SylowC3 ⋊ C11×D295

Subgroups

subgroupG/H
center, hypercenterC11D885
commutator, cosocle, hypocenterC3×C5×C59C2×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C59C2
LCSG ▷ C3×C5×C59
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9735

Conjugacy classes & character table

4884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 15);