Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10596410 |
| Fitting | C2×C32×C4 ⋊ SD16 |
| Sylow | C32 ⋊ C2×#460 |
702 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4⋊AGL(2,𝔽3), C2×D4×AΓL(1,𝔽9), #72220194, … |
| maximal normal subgroup of | C2×D4×AΓL(1,𝔽9), #72220194, #72220204, … |
| maximal quotient of | #72220194, #72220422, #72220446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99627);