Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#564 ⋊ C2 |
| Sylow | C7 ⋊ #3531 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×#564 | C2 |
| hypercenter | #564 | D7 |
| hypocenter | C7 | #3531 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #564 | |
930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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|b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dfg,h^a=h^6,c^b=cfg,d^b=df,h^d=h^6,h^e=h^695 conjugacy classes — view the full character table.
| maximal subgroup of | #13334991, #13334997, #13335002, … |
| maximal normal subgroup of | #13334991, #13334997, #13335002, … |
| maximal quotient of | #13516448, #13516472, #13516495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18973);