Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#67519 |
| Sylow | C32 ⋊ #1398 |
147 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #72222480, C3×#10682523, #72222493, … |
| maximal normal subgroup of | #72222480, C3×#10682523, #72222493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6687);