Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #2110 |
365 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 116 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=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,c^b=cg,d^b=dg,i^b=hi^2,h^c=h^2,i^c=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72222739, #72222742, #72222774, … |
| maximal normal subgroup of | #72222739, #72222742, #72222774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 29954);