Finite Group DatabasebetaFinite Group Databasebeta| order | 32512 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C24×C4 |
| direct product | C127×#14349 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C127 | C24 |
| commutator | C23 | C23×C4×C127 |
| Frattini, cosocle | C24 | C24×C127 |
| prime radical | C25×C127 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
1638 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1638 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16256 |
8128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32512, 7337);