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C3×#67272 #11764167

order1104
isoclinismisoclinic class of #67272
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×#67272

Splittings

FittingC3×D4×C23 ⋊ C2
HallC3×C23 ⋊ D8
SylowC23 ⋊ C3×D8

Subgroups

subgroupG/H
centerC2×C3C22⋊D23
commutator, cosocleC4×C23C22×C3
FrattiniC4C2×C3×D23
FittingC3×D4×C23C2
socleC2×C3×C23D4
hypercenterC3×D4D23
hypocenterC23C3×D8
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 552

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3)(4,5,7,9,11,13,15,17,19,21,23,25,26,24,22,20,18,16,14,12,10,8,6)(28,31)(29,34)(32,33);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,31)(30,33)(32,34)

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1104, 42);