Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D7×#578 |
| Fitting | C7×#578 ⋊ C2 |
| Sylow | C7 ⋊ C2×#578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D7 |
| commutator, cosocle | C4×C7 | C25 |
| Frattini | C4 | C24×D7 |
| Fitting | C7×#578 | C2 |
| socle | C2×C7 | C23×D4 |
| hypercenter | #578 | D7 |
| hypocenter | C7 | C2×#578 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2193, D7×#2195, #13507767, … |
| maximal normal subgroup of | D7×#2193, D7×#2195, #13507767, … |
| maximal quotient of | D7×#2898, D7×#2913, D7×#2947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19043);