Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #1948 |
386 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 81 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=f,b^2=fg,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=hi^2,d^b=dg,h^c=hi,i^c=hi^2,h^e=h^2,i^e=i^266 conjugacy classes — view the full character table.
| maximal subgroup of | #72269009, #106×GO+(4,𝔽2), #72269036 |
| maximal normal subgroup of | #72269009, #106×GO+(4,𝔽2), #72269036 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 24363);