Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ #2922 |
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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=e,f^2=g,b^a=be,h^a=h^6,d^b=dg,h^b=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | #13244484, #13244489, #13244494, … |
| maximal normal subgroup of | #13244484, #13244489, #13244494, … |
| maximal quotient of | #13351282, C4×#89901, C4×#89891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10730);