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C7×C79⋊C3 #13110304

order1659
isoclinismisoclinic class of C79⋊C3
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C79⋊C3
unambiguous semidirect productC79⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C79 ⋊ C3
derived, SylowC79 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC7C79⋊C3
commutator, cosocle, hypocenterC79C3×C7
FrattiniC1G
Fitting, socleC7×C79C3
LCSG ▷ C79
UCSC1 ◁ C7

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 86
transitive degreeμt(G) = 553

A minimal faithful permutation representation — 2 generators on 86 points:

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

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×C79⋊C3, C7×D79⋊C3, D7×C79⋊C3, …
maximal normal subgroup ofC2×C7×C79⋊C3, C7×D79⋊C3, D7×C79⋊C3, …
maximal quotient ofC2×C7×C79⋊C3, C49×C79⋊C3, C7×#13110305, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1659, 2);