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C13×D15×C59 #37527658

order23010
automorphism?
homologyAbelianization (H1) = C2×C13×C59 · Schur multiplier (H2) = C1

Aliases

direct productC13×D15×C59
unambiguous semidirect productC3⋊(D5×C13×C59)
unambiguous semidirect productC5⋊(D3×C13×C59)

Splittings

Fitting, socle, HallC3×C5×C13×C59 ⋊ C2
derived, HallC3×C5 ⋊ C2×C13×C59
HallC5×C13×C59 ⋊ D3
HallC3×C13×C59 ⋊ D5
HallC3×C5×C59 ⋊ C2×C13
HallC5×C59 ⋊ D3×C13
HallC3×C5×C13 ⋊ C2×C59
HallC3×C59 ⋊ D5×C13
HallC5×C13 ⋊ D3×C59
HallC3×C13 ⋊ D5×C59
SylowC5 ⋊ D3×C13×C59
SylowC3 ⋊ D5×C13×C59

Subgroups

subgroupG/H
center, hypercenterC13×C59D15
commutator, cosocle, hypocenterC3×C5C2×C13×C59
FrattiniC1G
Fitting, socleC3×C5×C13×C59C2
LCSG ▷ C3×C5
UCSC1 ◁ C13×C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11505

Conjugacy classes & character table

6903 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 14);