Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#504 ⋊ C2 |
| Sylow | C7 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D7 |
| commutator, socle | C2×C7 | C23×C8 |
| Fitting | C7×#504 | C2 |
| prime radical | D7×#41 | C4 |
| cosocle | C7×C8 | C24 |
| hypercenter | #504 | D7 |
| hypocenter | C7 | #3407 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C8 ◁ #504 | |
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 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,e^2=f,f^2=g,d^a=dg,c^b=cg,h^d=h^6188 conjugacy classes — view the full character table.
| maximal subgroup of | #13507039, #13507042, #13507046, … |
| maximal normal subgroup of | #13507039, #13507042, #13507046, … |
| maximal quotient of | #13506434, #13506444, #13506445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14223);