Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#63559 |
| Sylow | C32 ⋊ C4×#100 |
933 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 933 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10591503, C4×#10590397, C4×#10591522 |
| maximal normal subgroup of | C4×#10591503, C4×#10590397, C4×#10591522 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17800);