Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C7 ⋊ #1438 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D7 |
| commutator | C23×C7 | C22×C4 |
| Fitting, prime radical | C23×C7×D4 | C2 |
| socle, cosocle | C24×C7 | C23 |
| hypercenter | C23×D4 | D7 |
| hypocenter | C7 | #1438 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
1168 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 229 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=g,b^a=bd,c^a=ce,h^a=h^6,c^b=cf164 conjugacy classes — view the full character table.
| maximal subgroup of | #13241067, #13241069, #13241074, … |
| maximal normal subgroup of | #13241067, #13241069, #13241074, … |
| maximal quotient of | #13241718, #13241723, #13260284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4651);