Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C22 |
| Sylow | C32 ⋊ C2×#575 |
3117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|d^2=g,f^2=g,b^a=bf,c^a=cg,f^a=fg,i^a=hi^2,f^b=fg,i^b=hi^2,h^e=h^2,i^e=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72213893, #72214070, #72214997, … |
| maximal normal subgroup of | #72213893, #72214070, #72214997, … |
| maximal quotient of | #72222726 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152762);