Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#322 |
577 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 577 conjugacy classes of subgroups — too many to draw. Only its 184 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|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bf,i^a=hi^2,h^c=h^2,i^c=i^2192 conjugacy classes — view the full character table.
| maximal subgroup of | #72222657 |
| maximal normal subgroup of | #72222657 |
| maximal quotient of | #72222588 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7529);