Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #2492 |
814 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 123 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|a^2=eg,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^2i^2,i^a=h^2i,c^b=cg,h^b=hi,i^b=hi^2,i^c=hi^2,h^f=h^2,i^f=i^2,h^g=h^2,i^g=i^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 53126);