Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2295 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=f,c^2=fg,d^2=e,b^a=be,c^a=cfg,h^a=h^6,h^b=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | #13244430, #13244440, #13244450, … |
| maximal normal subgroup of | #13244430, #13244440, #13244450, … |
| maximal quotient of | #13274905, #13274925, C4×#89753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14662);