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C11×C79⋊C3 #14579658

order2607
isoclinismisoclinic class of C79⋊C3
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C79⋊C3
unambiguous semidirect productC79⋊(C3×C11)
unambiguous semidirect product(C11×C79)⋊C3

Splittings

Fitting, socle, HallC11×C79 ⋊ C3
derived, SylowC79 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC11C79⋊C3
commutator, cosocle, hypocenterC79C3×C11
FrattiniC1G
Fitting, socleC11×C79C3
LCSG ▷ C79
UCSC1 ◁ C11

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 90
transitive degreeμt(G) = 869

A minimal faithful permutation representation — 2 generators on 90 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,16)(15,18,23)(17,21,20)(19,25,33)(22,28,30)(24,31,27)(26,35,46)(29,38,43)(32,41,40)(34,44,37)(36,48,61)(39,51,59)(42,54,56)(45,57,53)(47,49,50)(52,64,74)(55,67,72)(58,70,69)(60,65,66)(62,75,63)(68,76,83)(71,79,81)(73,77,78)(80,84,88)(82,85,86)(87,89,90);(12,13,15,19,26,36,49,33,43,56,69,78,64,35,47,60,73,82,87,89,79,54,28,14,17,22,29,39,52,65,44,23,30,40,53,66,48,62,61,74,83,88,90,84,67,38,18,24,32,42,55,68,77,57,31,16,20,27,37,50,63,75,46,59,72,81,86,76,51,25,34,45,58,71,80,85,70,41,21)

Conjugacy classes & character table

319 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×C79⋊C3, C11⋊C5×C79⋊C3, C7×C11×C79⋊C3, …
maximal normal subgroup ofC5×C11×C79⋊C3, C11⋊C5×C79⋊C3, C7×C11×C79⋊C3, …
maximal quotient ofC5×C11×C79⋊C3, C7×C11×C79⋊C3, C11×#13110305, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2607, 1);