Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C23×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#386 |
3833 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=eg,b^a=be,c^a=cf,i^a=hi^2,h^d=h^2,i^d=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #72214860, #72252266, #72260305, … |
| maximal normal subgroup of | #72214860, #72252266, #72260305, … |
| maximal quotient of | #72214673, #72214713, #72214881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 35324);