Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #2971 |
402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=dg,h^a=h^6,c^b=cg,d^c=dg,h^c=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | #13249596, #13249600, #13249610, … |
| maximal normal subgroup of | #13249596, #13249600, #13249610, … |
| maximal quotient of | #13352086, #13352237, Q8×#6377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14730);