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C5×C13×D177 #37527655

order23010
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D177
unambiguous semidirect productC3⋊(C5×C13×D59)
unambiguous semidirect productC59⋊(C5×D3×C13)

Splittings

Fitting, socle, HallC3×C5×C13×C59 ⋊ C2
derived, HallC3×C59 ⋊ C2×C5×C13
HallC5×C13×C59 ⋊ D3
HallC3×C13×C59 ⋊ C2×C5
HallC3×C5×C59 ⋊ C2×C13
HallC13×C59 ⋊ C5×D3
HallC5×C59 ⋊ D3×C13
HallC3×C5×C13 ⋊ D59
SylowC59 ⋊ C5×D3×C13
HallC3×C13 ⋊ C5×D59
HallC3×C5 ⋊ C13×D59
SylowC3 ⋊ C5×C13×D59

Subgroups

subgroupG/H
center, hypercenterC5×C13D177
commutator, cosocle, hypocenterC3×C59C2×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C59C2
LCSG ▷ C3×C59
UCSC1 ◁ C5×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11505

Conjugacy classes & character table

5850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 11);