Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×Dic9 |
| Sylow | C9 ⋊ C4×H(5,𝔽2) |
2490 conjugacy classes of subgroups; only the 1440 normal subgroups are shown.
This group has 2490 conjugacy classes of subgroups — too many to draw. Only its 1440 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134180);