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C3×#87839 #11925396

order1200
isoclinismisoclinic class of #87837
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#87839

Splittings

HallC3×C52 ⋊ Q16
SylowC52 ⋊ C3×Q16

Subgroups

subgroupG/H
center, hypercenterC2×C3D52⋊C2
commutator, cosocle#1039C22×C3
FrattiniC2C3×D52⋊C2
Fitting, socle, prime radicalC2×C3×C52D4
hypocenterC52C3×Q16
LCSG ▷ #1039 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3

68 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)(4,12,6,10,11)(5,8)(7,13)(14,16,18,24)(15,19,21,28)(17,26,27,23)(20,29,25,22);(4,5)(6,9)(7,12)(8,11)(10,13)(14,15,18,21)(16,22,24,29)(17,25,27,20)(19,26,28,23)

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 606);