Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C32×C4⋊Q8 ⋊ C22 |
| Sylow | C32 ⋊ C2×#492 |
1457 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1457 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=hi^2,i^b=hi^2,h^d=h^2,i^d=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#492, #72243477, #72243765 |
| maximal normal subgroup of | D32×#492, #72243477, #72243765 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108169);