Finite Group Databasebeta

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C3×#90248 #13060900

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

Aliases

direct productC3×#90248

Splittings

FittingC3×C4×C7×D4 ⋊ C2
HallC3×C7 ⋊ #529
SylowC7 ⋊ C3×#529

Subgroups

subgroupG/H
centerC2×C3×C4C22×D7
commutator, cosocleC22×C7C24×C3
FrattiniC22C23×C3×D7
FittingC3×C4×C7×D4C2
socleC22×C3×C7C24
prime radicalC3×#6501C2
hypercenterC3×C4×D4D7
hypocenterC7C3×#529
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

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

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10189);