Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10588427 |
| Fitting | C2×C9×#100 ⋊ C2 |
| Sylow | C9 ⋊ C2×#453 |
1266 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×#453, C2×#10588427⋊C3, #72268983 |
| maximal normal subgroup of | C2×D9×#453, C2×#10588427⋊C3, #72268983 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98780);