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C2×C29×D37⋊C3 #27166152

order12876
isoclinismisoclinic class of D37⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C29×D37⋊C3
unambiguous semidirect productD37⋊(C2×C3×C29)
unambiguous semidirect product(C37⋊C3)⋊(C22×C29)
unambiguous semidirect product(C2×D37)⋊(C3×C29)
unambiguous semidirect product(C2×C37⋊C3)⋊(C2×C29)
unambiguous semidirect product(C2×C29×D37)⋊C3

Splittings

Fitting, socleC2×C29×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C22×C3×C29
HallC2×C29×D37 ⋊ C3
HallC29×C37⋊C3 ⋊ C22
HallC29×C37 ⋊ C22×C3
HallC2×D37 ⋊ C3×C29
HallC37⋊C3 ⋊ C22×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29D37⋊C3
commutator, cosocle, hypocenterC37C22×C3×C29
FrattiniC1G
Fitting, socleC2×C29×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C2×C29

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 68
transitive degreeμt(G) = 2146

A minimal faithful permutation representation — 2 generators on 68 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)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(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)(67,68)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C29×#66526⋊C2, D3×C29×D37⋊C3, C2×C3×C29×D37⋊C3, …
maximal normal subgroup ofC2×C29×#66526⋊C2, C2×C3×C29×D37⋊C3
maximal quotient ofC2×C29×#66524⋊C2, D3×C29×D37⋊C3, C2×C3×C29×D37⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 21);