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C5×#4294 #11719987

order855
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#4294

Splittings

derived, SylowC19 ⋊ C5×C9
HallC5×C19 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C19⋊C3
commutator, hypocenterC19C5×C9
FrattiniC3C5×C19⋊C3
Fitting, socle, prime radicalC3×C5×C19C3
cosocleC3×C19C3×C5
LCSG ▷ C19
UCSC1 ◁ C3×C5

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 855

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5)(7,8,10)(9,12,13)(11,15,14)(16,20,18)(17,21,19)(22,24,23)(25,26,28,27,29,31,30,32,33);(6,7,9,13,18,23,20,8,11,16,21,10,14,19,12,17,22,24,15)

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#4294⋊C2, D5×#4294, C5⋊(#4294⋊C2), …
maximal normal subgroup ofC5×#4294⋊C2, D5×#4294, C5⋊(#4294⋊C2), …
maximal quotient ofC2×C5×#4294, C5×C22⋊#4294, C25×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(855, 1);