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C5×#95⋊C9 #13083757

order1440
isoclinismisoclinic class of #95⋊C3
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×#95⋊C9
unambiguous semidirect product#95⋊(C5×C9)
unambiguous semidirect product(C5×#95)⋊C9

Splittings

derived, Sylow#95 ⋊ C5×C9
HallC5×#95 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C42⋊C3
commutator, hypocenter#95C5×C9
FrattiniC23×C3C5×A4
FittingC3×C5×#95C3
socle, prime radicalC23×C3×C5A4
cosocleC3×#95C3×C5
LCSG ▷ #95
UCSC1 ◁ C2×C3×C5

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 180

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5)(6,7,10)(8,12,17)(9,13,16)(11,15,14)(18,19,21,20,22,24,23,25,26);(6,8,9,14)(10,15)(11,12)(16,17)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 74);