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C5×(C151⋊C5)⋊C9 #46800844

order33975
automorphism?
homologyAbelianization (H1) = C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×(C151⋊C5)⋊C9
unambiguous semidirect product(C151⋊C5)⋊(C5×C9)
unambiguous semidirect product(C151⋊C9)⋊C52
unambiguous semidirect product(C5×C151⋊C5)⋊C9
unambiguous semidirect product(C5×C151⋊C9)⋊C5

Splittings

derived, SylowC151 ⋊ C52×C9
HallC5×C151⋊C5 ⋊ C9
HallC151⋊C9 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC3×C5(C151⋊C3)⋊C5
commutator, hypocenterC151C52×C9
FrattiniC3C5×(C151⋊C3)⋊C5
Fitting, socleC3×C5×C151C3×C5
prime radicalC3×C5×C151⋊C5C3
cosocleC3×C151C3×C52
LCSG ▷ C151
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6795

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33975, 12);