Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×H(5,𝔽2) ⋊ C22 |
| Sylow | C32 ⋊ #3292 |
1036 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|b^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,i^a=h^2i,c^b=cg,d^b=de,e^b=eg,f^c=fg,i^c=hi^2,e^d=eg,h^d=h^2,i^d=h^2i90 conjugacy classes — view the full character table.
| maximal subgroup of | #72214920, #72214930, #72214946 |
| maximal normal subgroup of | #72214920, #72214930, #72214946 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 120923);