Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | S4×ΓL(1,𝔽25) |
| Fitting | C22×C3×C8 ⋊ C2×D3 |
614 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#914, S4×#911, D3×M16×S4, … |
| maximal normal subgroup of | S4×#914, S4×#911, D3×M16×S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155797);