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C29×C22⋊(C37⋊C3) #27166174

order12876
isoclinismisoclinic class of C22⋊(C37⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC29×C22⋊(C37⋊C3)
unambiguous semidirect productC22⋊(C29×C37⋊C3)
unambiguous semidirect productC37⋊(A4×C29)
unambiguous semidirect product(C22×C29)⋊(C37⋊C3)
unambiguous semidirect product(C29×C37)⋊A4

Splittings

Fitting, socle, HallC22×C29×C37 ⋊ C3
derived, HallC22×C37 ⋊ C3×C29
HallC29×C37 ⋊ A4
HallC22×C29 ⋊ C37⋊C3
SylowC37 ⋊ A4×C29
SylowC22 ⋊ C29×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC29C22⋊(C37⋊C3)
commutator, cosocle, hypocenterC22×C37C3×C29
FrattiniC1G
Fitting, socleC22×C29×C37C3
LCSG ▷ C22×C37
UCSC1 ◁ C29

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 4292

A minimal faithful permutation representation — 2 generators on 70 points:

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

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C29×C37⋊C3, C3×C29×C22⋊(C37⋊C3)
maximal normal subgroup ofA4×C29×C37⋊C3, C3×C29×C22⋊(C37⋊C3)
maximal quotient ofC29×C22⋊#66524, C3×C29×C22⋊(C37⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 43);