Finite Group Databasebeta

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C5×C13⋊C3×C179 #46853249

order34905
automorphism?
homologyAbelianization (H1) = C3×C5×C179 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊C3×C179
unambiguous semidirect productC13⋊(C3×C5×C179)
unambiguous semidirect product(C5×C13)⋊(C3×C179)
unambiguous semidirect product(C13×C179)⋊(C3×C5)
unambiguous semidirect product(C5×C13×C179)⋊C3

Splittings

Fitting, socle, HallC5×C13×C179 ⋊ C3
derived, SylowC13 ⋊ C3×C5×C179
HallC13×C179 ⋊ C3×C5
HallC5×C13 ⋊ C3×C179

Subgroups

subgroupG/H
center, hypercenterC5×C179C13⋊C3
commutator, cosocle, hypocenterC13C3×C5×C179
FrattiniC1G
Fitting, socleC5×C13×C179C3
LCSG ▷ C13
UCSC1 ◁ C5×C179

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11635

Conjugacy classes & character table

6265 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34905, 2);