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C5×C43⋊C9 #14515403

order1935
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C43⋊C9
unambiguous semidirect productC43⋊(C5×C9)
unambiguous semidirect product(C5×C43)⋊C9

Splittings

derived, SylowC43 ⋊ C5×C9
HallC5×C43 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C43⋊C3
commutator, hypocenterC43C5×C9
FrattiniC3C5×C43⋊C3
Fitting, socle, prime radicalC3×C5×C43C3
cosocleC3×C43C3×C5
LCSG ▷ C43
UCSC1 ◁ C3×C5

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 1935

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5)(7,8,10)(9,12,17)(11,15,14)(13,19,27)(16,22,24)(18,25,21)(20,29,38)(23,31,36)(26,34,33)(28,37,30)(32,41,45)(35,42,44)(39,46,40)(43,47,48)(49,50,52,51,53,55,54,56,57);(6,7,9,13,20,25,10,14,21,30,40,37,17,24,33,29,39,46,27,36,44,41,19,28,38,45,48,47,31,12,18,26,35,43,42,22,8,11,16,23,32,34,15)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D43⋊C9, D5×C43⋊C9, C5⋊(D43⋊C9), …
maximal normal subgroup ofC5×D43⋊C9, D5×C43⋊C9, C5⋊(D43⋊C9), …
maximal quotient ofC2×C5×C43⋊C9, C5×C7×C43⋊C9, C5×#14582151, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1935, 1);