Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C83 · Schur multiplier (H2) = C211 |
| direct product | C23×#99×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C83 | C22⋊C4 |
| commutator | C22 | C24×C4×C83 |
| Frattini, cosocle | C23 | C25×C83 |
| prime radical | C24×D4×C83 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C83 ◁ C26×C83 ◁ G | |
7902 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
7304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 53054);