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D29×D37⋊C3 #27166151

order12876
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD29×D37⋊C3
unambiguous semidirect productD37⋊(C3×D29)
unambiguous semidirect product(D29×D37)⋊C3
unambiguous semidirect product(C29×D37⋊C3)⋊C2
unambiguous semidirect product(D29×C37⋊C3)⋊C2
unambiguous semidirect product(C29⋊(D37⋊C3))⋊C2

Splittings

Fitting, socle, derived, HallC29×C37 ⋊ C22×C3
HallD29×D37 ⋊ C3
HallC29×C37⋊C3 ⋊ C22
HallC37⋊C3 ⋊ C2×D29
SylowC37 ⋊ C2×C3×D29
SylowC29 ⋊ C2×D37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC29×C37C22×C3
LCSG ▷ C29×C37
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 1073

A minimal faithful permutation representation — 2 generators on 66 points:

(2,6,7,3,4,8)(5,14,15,9,10,23)(11,26,27,17,18,34)(12,25,21,19,16,13)(20,36,37,29,28,32)(22,24,35,31,30,33)(38,39,41,43,45,47,49,51,53,55,57,59,61,63,65,66,64,62,60,58,56,54,52,50,48,46,44,42,40);(1,2,5,11,18,28,33,34,31,21,7,6,12,20,30,10,16,23,32,37,15,25,14,24,29,19,4,8,13,22,27,35,36,26,17,9,3)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD29×#66526⋊C2, C3×D29×D37⋊C3, D87×D37⋊C3, …
maximal normal subgroup ofD29×#66526⋊C2, C3×D29×D37⋊C3
maximal quotient ofD29×#66524⋊C2, C3×D29×D37⋊C3, D87×D37⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 20);