Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| isoclinism | isoclinic class of D87 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D87 |
| Fitting, socle | C23×C3×C29 ⋊ C2 |
| derived, Hall | C3×C29 ⋊ C24 |
| Sylow | C29 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D87 |
| commutator, cosocle, hypocenter | C3×C29 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C29 | C2 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C23 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 696 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 197);