Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D7×#551 |
| Fitting | C7×#551 ⋊ C2 |
| Sylow | C7 ⋊ C2×#551 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×#551 | C2 |
| prime radical | D7×#120 | C2 |
| hypercenter | #551 | D7 |
| hypocenter | C7 | C2×#551 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #551 | |
1328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2197, C2×D7×#551, D7×#3475, … |
| maximal normal subgroup of | D7×#2197, C2×D7×#551, D7×#3475, … |
| maximal quotient of | D7×#2342, D7×#2343, D7×#2353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18648);