Finite Group Databasebeta

← Prev (#13060941) Next (#13060943) →

C3×#90291 #13060942

order1344
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#90291

Splittings

HallC3×C7 ⋊ #529
SylowC7 ⋊ C3×#529

Subgroups

subgroupG/H
centerC22×C3C23×D7
commutator, cosocleC22×C7C24×C3
FrattiniC22C23×C3×D7
Fitting, prime radicalC3×C7×#121C2
socleC22×C3×C7C24
hypercenterC3×#121D7
hypocenterC7C3×#529
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C3 ◁ C3×#121

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 672

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10231);