Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C32×#124 ⋊ C22 |
| Sylow | C32 ⋊ C2×#496 |
1501 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1501 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
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,c^b=cg,i^b=hi^2,h^d=h^2,i^d=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72243765, D32×#496, #72252606 |
| maximal normal subgroup of | #72243765, D32×#496, #72252606 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108363);