Finite Group Databasebeta

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C3×C7⋊#401 #13055091

order1344
isoclinismisoclinic class of #89428
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×C7⋊#401

Splittings

HallC3×C7 ⋊ #401
SylowC7 ⋊ C3×#401

Subgroups

subgroupG/H
centerC23×C3C22×D7
commutator, cosocleC23×C7C23×C3
FrattiniC23C22×C3×D7
FittingC3×C7×#95C2
socle, prime radicalC23×C3×C7C23
hypercenterC3×#95D7
hypocenterC7C3×#401
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C3 ◁ C3×#95

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 1344

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4380);