Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C2×C32×#120 ⋊ C2 |
| Sylow | C32 ⋊ #2021 |
1914 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1914 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^c=dg,h^c=h^2,i^c=i^2138 conjugacy classes — view the full character table.
| maximal subgroup of | #72214737, #72214841 |
| maximal normal subgroup of | #72214737, #72214841 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26797);