Finite Group DatabasebetaFinite Group Databasebeta| order | 1632 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C17 ⋊ #121 |
| Sylow | C17 ⋊ #895 |
| Sylow | C3 ⋊ #10587625 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D17 |
| commutator, socle, cosocle | C22×C3×C17 | C23 |
| Fitting | C2×C3×C4×C17 | C22 |
| hypercenter | C2×C4 | D3×D17 |
| hypocenter | C3×C17 | #121 |
| LCS | G ▷ C22×C3×C17 ▷ C3×C17 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
188 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 816 |
Polycyclic presentation:
2^5,3,17|a^2=e,c^2=d,c^a=ce,g^a=g^16,c^b=cd,f^b=f^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1632, 465);