Finite Group DatabasebetaFinite Group Databasebeta| order | 16884 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #22554729⋊C2 |
| unambiguous semidirect product | #22554733⋊C2 |
| unambiguous semidirect product | #22554737⋊C2 |
| derived, Hall | C7×C67 ⋊ C22×C9 |
| Hall | #16862451 ⋊ C22 |
| Hall | D7×D67 ⋊ C9 |
| Sylow | C67 ⋊ C2×D7⋊C9 |
| Sylow | C7 ⋊ C2×D67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14584196⋊C2 |
| commutator, hypocenter | C7×C67 | C22×C9 |
| Fitting, socle, cosocle | C3×C7×C67 | C22×C3 |
| prime radical | C3×D7×D67 | C3 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4221 |
Polycyclic presentation:
2^2,3,7,67,3|c^3=f,e^a=e^66,d^b=d^6,d^c=d^2,e^c=e^29207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16884, 26);