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C13×C71⋊C5 #17987223

order4615
isoclinismisoclinic class of C71⋊C5
automorphism?
homologyAbelianization (H1) = C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C71⋊C5
unambiguous semidirect productC71⋊(C5×C13)
unambiguous semidirect product(C13×C71)⋊C5

Splittings

Fitting, socle, HallC13×C71 ⋊ C5
derived, SylowC71 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC13C71⋊C5
commutator, cosocle, hypocenterC71C5×C13
FrattiniC1G
Fitting, socleC13×C71C5
LCSG ▷ C71
UCSC1 ◁ C13

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 84
transitive degreeμt(G) = 923

A minimal faithful permutation representation — 2 generators on 84 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16,18,22,30)(17,20,26,37,52)(19,24,34,38,43)(21,28,41,58,29)(23,32,45,31,44)(25,36,51,70,71)(27,39,55,73,62)(33,47,66,53,72)(35,49,59,54,63)(40,57,76,61,80)(42,60,78,50,69)(46,65,48,56,64)(67,83,74,84,81)(68,79,77,75,82);(14,15,17,21,29,18,23,33,44,63,26,38,54,65,82,41,59,77,83,84,28,42,61,47,67,30,43,62,69,58,45,64,81,72,78,66,73,20,27,40,32,46,36,37,53,49,68,57,55,74,52,71,80,76,16,19,25,22,31,24,35,50,34,48,39,56,75,51,70,60,79)

Conjugacy classes & character table

247 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C13×C71⋊C5, C13⋊C3×C71⋊C5, C5×C13×C71⋊C5, …
maximal normal subgroup ofC3×C13×C71⋊C5, C13⋊C3×C71⋊C5, C5×C13×C71⋊C5, …
maximal quotient ofC3×C13×C71⋊C5, C13×C71⋊C25, C5×C13×C71⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4615, 1);