Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C32×Q16 ⋊ C22 |
| Sylow | C32 ⋊ C2×#470 |
1113 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 1113 conjugacy classes of subgroups — too many to draw. Only its 176 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=g,b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,i^c=hi^2,h^d=h^2,i^d=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 101019);