Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #4621 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#4621 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | #857 |
| commutator, cosocle, hypocenter | #95⋊C3 | C2×C7 |
| Frattini | C23 | C7×S4 |
| Fitting | C7×#95 | D3 |
| socle | C23×C7 | S4 |
| prime radical | C7×#95⋊C3 | C2 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C2×C7 | |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 168 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,21,14,12,15,11,26)(10,28,20,27)(13,22,23,30)(16,18)(17,25,31,24)(19,29);(8,10,17)(9,13,16)(11,18,31)(12,20,22)(14,25,28)(15,24,29)(19,30,21)(23,27,26)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 819);