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C3×C5×C59⋊C29 #38787248

order25665
automorphism?
homologyAbelianization (H1) = C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C59⋊C29
unambiguous semidirect productC59⋊(C3×C5×C29)
unambiguous semidirect product(C3×C59)⋊(C5×C29)
unambiguous semidirect product(C5×C59)⋊(C3×C29)
unambiguous semidirect product(C3×C5×C59)⋊C29

Splittings

Fitting, socle, HallC3×C5×C59 ⋊ C29
derived, SylowC59 ⋊ C3×C5×C29
HallC5×C59 ⋊ C3×C29
HallC3×C59 ⋊ C5×C29

Subgroups

subgroupG/H
center, hypercenterC3×C5C59⋊C29
commutator, cosocle, hypocenterC59C3×C5×C29
FrattiniC1G
Fitting, socleC3×C5×C59C29
LCSG ▷ C59
UCSC1 ◁ C3×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 885

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25665, 2);