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C3×C22⋊D37 #11725173

order888
isoclinismisoclinic class of Dic74
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×C22⋊D37

Splittings

FittingC22×C3×C37 ⋊ C2
HallC3×C37 ⋊ D4
SylowC37 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D37
commutator, cosocleC2×C37C22×C3
FrattiniC2C2×C3×D37
FittingC22×C3×C37C2
socleC2×C3×C37C22
hypercenterC22×C3D37
hypocenterC37C3×D4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C3 ◁ C22×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 444

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13183974, #13183975, D3×C22⋊D37, …
maximal normal subgroup of#13183974, #13183975, D3×C22⋊D37, …
maximal quotient ofC3×#10596936, C3×#10596938, C3×#10596939, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(888, 31);