Finite Group DatabasebetaFinite Group Databasebeta| order | 12736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C199 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊C4×C199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C199 | C22 |
| commutator | C2 | C23×C4×C199 |
| Frattini, cosocle | C22 | C24×C199 |
| prime radical | C25×C199 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C199 ◁ G | |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6368 |
7960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12736, 193);