Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #1580 |
576 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=e,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^2,i^a=i^2,d^b=df,h^c=h^2,i^c=i^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #72222464, C3⋊D3×#1580, #72222571, … |
| maximal normal subgroup of | #72222464, C3⋊D3×#1580, #72222571, … |
| maximal quotient of | #72222464, C2×#11777340, #72255421 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 11351);