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C3×#87809 #11925202

order1200
isoclinismisoclinic class of #87809
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC3×#87809

Splittings

FittingC3×C52×D4 ⋊ C2
HallC3×C52 ⋊ D8
SylowC52 ⋊ C3×D8

Subgroups

subgroupG/H
centerC2×C3C22⋊(C5⋊D5)
commutator, cosocleC4×C52C22×C3
FrattiniC4C2×C3×C5⋊D5
FittingC3×C52×D4C2
socleC2×C3×C52D4
hypercenterC3×D4C5⋊D5
hypocenterC52C3×D8
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 600

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2,3)(5,8)(6,11)(9,10)(17,18,20,21,19);(4,5)(6,8)(7,10)(9,11)(13,14)(15,16)(18,19)(20,21);(12,13,15,16,14)

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 412);