Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C32×C17 ⋊ D4 |
| Sylow | C17 ⋊ #625 |
| Sylow | C32 ⋊ C22⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D51 |
| commutator, Fitting, socle, cosocle | C2×C32×C17 | C22 |
| hypocenter | C32×C17 | D4 |
| LCS | G ▷ C2×C32×C17 ▷ C32×C17 | |
| UCS | C1 ◁ C2 | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 408 |
Polycyclic presentation:
2^3,3^2,17|b^a=bc,d^a=d^2,f^a=f^16,e^b=e^2159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 81);