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C13×D885 #37527659

order23010
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D885
unambiguous semidirect productC3⋊(C13×D295)
unambiguous semidirect productC5⋊(C13×D177)
unambiguous semidirect productC59⋊(C13×D15)

Splittings

Fitting, socle, HallC3×C5×C13×C59 ⋊ C2
derived, HallC3×C5×C59 ⋊ C2×C13
HallC5×C13×C59 ⋊ D3
HallC3×C13×C59 ⋊ D5
HallC13×C59 ⋊ D15
HallC5×C59 ⋊ D3×C13
HallC3×C5×C13 ⋊ D59
HallC3×C59 ⋊ D5×C13
HallC5×C13 ⋊ D177
SylowC59 ⋊ C13×D15
HallC3×C13 ⋊ D295
HallC3×C5 ⋊ C13×D59
SylowC5 ⋊ C13×D177
SylowC3 ⋊ C13×D295

Subgroups

subgroupG/H
center, hypercenterC13D885
commutator, cosocle, hypocenterC3×C5×C59C2×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C59C2
LCSG ▷ C3×C5×C59
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11505

Conjugacy classes & character table

5772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 15);