Finite Group DatabasebetaFinite Group Databasebeta| order | 22976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D359 |
| Fitting | M32×C359 ⋊ C2 |
| Sylow | C359 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D359 |
| commutator, socle | C2×C359 | C22×C8 |
| Fitting | M32×C359 | C2 |
| prime radical | C22×D359 | C8 |
| cosocle | C8×C359 | C23 |
| hypercenter | M32 | D359 |
| hypocenter | C359 | C2×M32 |
| LCS | G ▷ C2×C359 ▷ C359 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5744 |
3620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22976, 962);