Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C7⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×C7⋊#226 |
| Sylow | C7 ⋊ C22×#226 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C7⋊S4 |
| commutator, cosocle, hypocenter | C7×SL(2,𝔽3) | C23 |
| Frattini | C2 | C22×C7⋊S4 |
| Fitting | C22×C7×Q8 | D3 |
| socle | C23×C7 | S4 |
| prime radical | C22×C7×SL(2,𝔽3) | C2 |
| LCS | G ▷ C7×SL(2,𝔽3) | |
| UCS | C1 ◁ C23 | |
306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11401);