Finite Group DatabasebetaFinite Group Databasebeta| order | 27392 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C107 · Schur multiplier (H2) = C29 |
| direct product | C107×#13794 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C107 | C24 |
| commutator | C22 | C22×C42×C107 |
| Frattini, cosocle | C24 | C24×C107 |
| prime radical | C26×C107 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C107 ◁ G | |
4462 conjugacy classes of subgroups; only the 1214 normal subgroups are shown.
This group has 4462 conjugacy classes of subgroups — too many to draw. Only its 1214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6848 |
9416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27392, 6782);