Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C7×#121 ⋊ C2 |
| Sylow | C7 ⋊ #1999 |
496 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 95 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|d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^6,c^b=cf,d^b=dg116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1999, C2×#11729438, #13380598, … |
| maximal normal subgroup of | D7×#1999, C2×#11729438, #13380598, … |
| maximal quotient of | #13253990, #13253992, #13253997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4204);