Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10588421 |
| Fitting | C2×C9×#99 ⋊ C2 |
| Sylow | C9 ⋊ C2×B(4,𝔽2) |
1527 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 1527 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×B(4,𝔽2), #72268777, #72268793, … |
| maximal normal subgroup of | C2×D9×B(4,𝔽2), #72268777, #72268793, … |
| maximal quotient of | #72268777, #72268793 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99261);