Finite Group DatabasebetaFinite Group Databasebeta| order | 22976 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×Dic359 |
| unambiguous semidirect product | C359⋊C43 |
| derived, Sylow | C359 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D359 |
| commutator, hypocenter | C359 | C43 |
| Frattini | C23 | C22×D359 |
| Fitting | C2×C42×C359 | C2 |
| socle, prime radical, cosocle | C23×C359 | C23 |
| LCS | G ▷ C359 | |
| UCS | C1 ◁ C2×C42 | |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22976 |
5792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22976, 391);