Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C7×#95 ⋊ C2 |
| Sylow | C7 ⋊ #1440 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D7 |
| commutator | C23×C7 | C22×C4 |
| Fitting | C2×C7×#95 | C2 |
| socle, cosocle | C24×C7 | C23 |
| prime radical | C24×D7 | C22 |
| hypercenter | C2×#95 | D7 |
| hypocenter | C7 | #1440 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
736 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,c^2=d,b^a=bd,c^a=ce,c^b=cf,h^b=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1440, C2×#11727183, #13275474, … |
| maximal normal subgroup of | D7×#1440, C2×#11727183, #13275474, … |
| maximal quotient of | #13241717, #13241720, #13241721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1949);