Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | C2×C4×#3787 |
| derived, Sylow | C32 ⋊ C22×C4×C8 |
1258 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91116);