Finite Group DatabasebetaFinite Group Databasebeta| order | 12736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C199 · Schur multiplier (H2) = C25 |
| direct product | #546×C199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C199 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C199 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C199 ◁ G | |
334 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3184 |
4975 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3264×C199, #3266×C199, #3267×C199, … |
| maximal normal subgroup of | #3264×C199, #3266×C199, #3267×C199, … |
| maximal quotient of | D4×C22⋊C4×C199, #2339×C199, #2342×C199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12736, 227);