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C5×D2301 #37527657

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

Aliases

direct productC5×D2301
unambiguous semidirect productC3⋊(C5×D767)
unambiguous semidirect productC13⋊(C5×D177)
unambiguous semidirect productC59⋊(C5×D39)

Splittings

Fitting, socle, HallC3×C5×C13×C59 ⋊ C2
derived, HallC3×C13×C59 ⋊ C2×C5
HallC5×C13×C59 ⋊ D3
HallC3×C5×C59 ⋊ D13
HallC13×C59 ⋊ C5×D3
HallC5×C59 ⋊ D39
HallC3×C5×C13 ⋊ D59
HallC3×C59 ⋊ C5×D13
HallC5×C13 ⋊ D177
SylowC59 ⋊ C5×D39
HallC3×C13 ⋊ C5×D59
HallC3×C5 ⋊ D767
SylowC13 ⋊ C5×D177
SylowC3 ⋊ C5×D767

Subgroups

subgroupG/H
center, hypercenterC5D2301
commutator, cosocle, hypocenterC3×C13×C59C2×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C59C2
LCSG ▷ C3×C13×C59
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11505

Conjugacy classes & character table

5760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 13);