Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #1883 |
869 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,i^a=hi^2,d^b=dg,f^b=fg,i^b=hi^2,e^c=eg,h^c=h^2,i^c=h^2i96 conjugacy classes — view the full character table.
| maximal subgroup of | #72259774, #72259840, C4×#10591522 |
| maximal normal subgroup of | #72259774, #72259840, C4×#10591522 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 21752);