Finite Group DatabasebetaFinite Group Databasebeta| order | 28322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C17⋊D833 |
| unambiguous semidirect product | C49⋊(C17⋊D17) |
| Fitting, derived, Hall | C172×C49 ⋊ C2 |
| Sylow | C172 ⋊ D49 |
| Sylow | C49 ⋊ C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C172×C49 | C2 |
| Frattini | C7 | C7⋊(C17⋊D17) |
| socle | C7×C172 | D7 |
| LCS | G ▷ C172×C49 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14161 |
Polycyclic presentation:
2,7,17^2,7|b^7=e^6,b^a=b^6e,c^a=c^16,d^a=d^16,e^a=e^67082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28322, 16);