Finite Group DatabasebetaFinite Group Databasebeta| order | 12736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C199 · Schur multiplier (H2) = C23 |
| direct product | #395×C199 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C199 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C199 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C199 ◁ G | |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12736 |
4378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12736, 76);