Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#432 ⋊ C2 |
| Sylow | C7 ⋊ #1527 |
264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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|a^2=e,d^2=g,e^2=f,b^a=bd,c^a=cf,d^a=df,h^a=h^6,d^b=dg,e^b=efg,h^b=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13245418, #13245420, #13245423, … |
| maximal normal subgroup of | #13245418, #13245420, #13245423, … |
| maximal quotient of | #13241782, #13241795, #13241839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3324);