Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #2405 |
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 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) = 224 |
Polycyclic presentation:
2^7,7|c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^6,c^b=cg158 conjugacy classes — view the full character table.
| maximal subgroup of | #13251698, #13251700, #13251708, … |
| maximal normal subgroup of | #13251698, #13251700, #13251708, … |
| maximal quotient of | #13275662, #13275680, #13276577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14337);