Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ #2021 |
1607 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|b^a=bd,c^a=ce,f^a=fg,h^a=h^2,i^a=i^2,c^b=cf,h^b=h^2,i^b=i^2,d^c=dg,i^c=hi^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72252340, #72252343, #72252346 |
| maximal normal subgroup of | #72252340, #72252343, #72252346 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26816);