Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C7×#125 ⋊ C2 |
| Sylow | C7 ⋊ #3080 |
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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=e,b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^c=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13250884, #13250890, #13250891, … |
| maximal normal subgroup of | #13250884, #13250890, #13250891, … |
| maximal quotient of | #13353294, #13354771, #13355975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15228);