Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of #157⋊D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #157⋊D17 |
| Fitting, socle, Hall | C32×C17 ⋊ D4 |
| Sylow | C17 ⋊ GO+(4,𝔽2) |
| Sylow | C32 ⋊ D68 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C17×C3⋊D3 | C22 |
| Fitting, socle, hypocenter | C32×C17 | D4 |
| LCS | G ▷ C17×C3⋊D3 ▷ C32×C17 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 102 |
Polycyclic presentation:
2^3,3^2,17|b^2=c,b^a=bc,d^a=d^2,f^a=f^16,d^b=e^2,e^b=d,d^c=d^2,e^c=e^257 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 136);