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C3×#87775 #11925067

order1200
isoclinismisoclinic class of #87770
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#87775

Splittings

HallC3×C52 ⋊ Q16
SylowC52 ⋊ C3×Q16

Subgroups

subgroupG/H
centerC2×C3#6037
commutator, cosocleC4×C52C22×C3
FrattiniC4C3×D52
FittingC3×C4×C52C22
socle, prime radicalC2×C3×C52D4
hypercenterC3×C4D52
hypocenterC52C3×Q16
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C3×C4

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 277);