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C7×D79⋊C3 #15693296

order3318
isoclinismisoclinic class of D79⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D79⋊C3
unambiguous semidirect productD79⋊(C3×C7)
unambiguous semidirect product(C79⋊C3)⋊(C2×C7)

Splittings

Fitting, socle, HallC7×C79 ⋊ C2×C3
derived, SylowC79 ⋊ C2×C3×C7
HallC7×C79⋊C3 ⋊ C2
HallC7×D79 ⋊ C3
HallC79⋊C3 ⋊ C2×C7
HallD79 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC7D79⋊C3
commutator, cosocle, hypocenterC79C2×C3×C7
FrattiniC1G
Fitting, socleC7×C79C2×C3
LCSG ▷ C79
UCSC1 ◁ C7

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

Conjugacy classes & character table

133 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7×D79⋊C3, C7×C5⋊(D79⋊C3), C49×D79⋊C3, …
maximal normal subgroup ofC5×C7×D79⋊C3, C49×D79⋊C3, C72×D79⋊C3, …
maximal quotient ofC5×C7×D79⋊C3, C7×C5⋊(D79⋊C3), C49×D79⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3318, 13);