Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4⋊C4×GO+(4,𝔽2) |
| Fitting | C32×C4⋊C4 ⋊ D4 |
| Sylow | C32 ⋊ D4×C4⋊C4 |
1194 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C4×AΓL(1,𝔽9), #106×GO+(4,𝔽2), #72269025 |
| maximal normal subgroup of | C4⋊C4×AΓL(1,𝔽9), #106×GO+(4,𝔽2), #72269025 |
| maximal quotient of | #106×GO+(4,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 39483);