Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#81791 |
| Fitting | C32×#493 ⋊ C2 |
| Sylow | C32 ⋊ #3292 |
1033 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1033 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11671493, #72214310, #72214341, … |
| maximal normal subgroup of | C3×#11671493, #72214310, #72214341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 120913);