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C5×C31⋊C9 #13063695

order1395
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C31⋊C9
unambiguous semidirect product(C5×C31)⋊C9

Splittings

derived, SylowC31 ⋊ C5×C9
HallC5×C31 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C31⋊C3
commutator, hypocenterC31C5×C9
FrattiniC3C5×C31⋊C3
Fitting, socle, prime radicalC3×C5×C31C3
cosocleC3×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C3×C5

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 1395

A minimal faithful permutation representation — 2 generators on 45 points:

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D31⋊C9, D5×C31⋊C9, C5⋊(D31⋊C9), …
maximal normal subgroup ofC5×D31⋊C9, D5×C31⋊C9, C5⋊(D31⋊C9), …
maximal quotient ofC2×C5×C31⋊C9, C5×C11×C31⋊C9, C11⋊C5×C31⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1395, 3);