Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C97 · Schur multiplier (H2) = C24×C4 |
| direct product | C97×#2274 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C97 | C24 |
| commutator | C2 | C22×C42×C97 |
| Frattini, cosocle | C23 | C24×C97 |
| prime radical | C24×C97 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C97 ◁ G | |
696 conjugacy classes of subgroups; only the 520 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 520 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6208 |
6596 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 1006);