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Cayley diagram

C3×C49⋊C3 #89201

order441
isoclinismisoclinic class of C49⋊C3
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C49⋊C3
unambiguous semidirect productC49⋊C32
unambiguous semidirect product(C3×C49)⋊C3

Splittings

FittingC3×C49 ⋊ C3
derived, SylowC49 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3C49⋊C3
commutator, cosocle, hypocenterC49C32
FrattiniC7C3×ΓL(1,𝔽8)
FittingC3×C49C3
socleC3×C7ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C3

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 147

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D49⋊C3, D3×C49⋊C3, C3⋊(D49⋊C3), …
maximal normal subgroup ofC3×D49⋊C3, D3×C49⋊C3, C3⋊(D49⋊C3), …
maximal quotient ofC2×C3×C49⋊C3, C9×C49⋊C3, #13050484, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(441, 3);