Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#331 ⋊ C2 |
| Sylow | C7 ⋊ #1402 |
122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|a^2=d,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^6,d^b=deg,e^b=eg,f^b=fg,h^b=h^6,d^c=dfg,e^c=eg,e^d=eg74 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1402, C2×#11725268, #13274013, … |
| maximal normal subgroup of | D7×#1402, C2×#11725268, #13274013, … |
| maximal quotient of | #13241156, #13241223, #13241322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 34);