Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ C4×AGL(1,ℤ/8) |
1162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,i^a=h^2i,e^b=eg,i^c=hi^2,h^d=h^2,i^d=h^2i108 conjugacy classes — view the full character table.
| maximal subgroup of | #72222689, #72227388, #72227391 |
| maximal normal subgroup of | #72222689, #72227388, #72227391 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 94301);