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C5×C59×D39 #37527656

order23010
automorphism?
homologyAbelianization (H1) = C2×C5×C59 · Schur multiplier (H2) = C1

Aliases

direct productC5×C59×D39
unambiguous semidirect productC3⋊(C5×D13×C59)
unambiguous semidirect productC13⋊(C5×D3×C59)

Splittings

Fitting, socle, HallC3×C5×C13×C59 ⋊ C2
derived, HallC3×C13 ⋊ C2×C5×C59
HallC5×C13×C59 ⋊ D3
HallC3×C13×C59 ⋊ C2×C5
HallC3×C5×C59 ⋊ D13
HallC13×C59 ⋊ C5×D3
HallC3×C5×C13 ⋊ C2×C59
HallC3×C59 ⋊ C5×D13
HallC5×C13 ⋊ D3×C59
HallC3×C5 ⋊ D13×C59
SylowC13 ⋊ C5×D3×C59
SylowC3 ⋊ C5×D13×C59

Subgroups

subgroupG/H
center, hypercenterC5×C59D39
commutator, cosocle, hypocenterC3×C13C2×C5×C59
FrattiniC1G
Fitting, socleC3×C5×C13×C59C2
LCSG ▷ C3×C13
UCSC1 ◁ C5×C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11505

Conjugacy classes & character table

6195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 12);