Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#67791 |
| Sylow | C32 ⋊ #1357 |
305 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10708578, #72214603, C3×#10708954, … |
| maximal normal subgroup of | C3×#10708578, #72214603, C3×#10708954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6021);