Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D7×#556 |
| Fitting | C7×#556 ⋊ C2 |
| Sylow | C7 ⋊ C2×#556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×#556 | C2 |
| prime radical | C2×D4×D7 | C22 |
| hypercenter | #556 | D7 |
| hypocenter | C7 | C2×#556 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #556 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1628, D7×#1638, D7×#1652, … |
| maximal normal subgroup of | D7×#1628, D7×#1638, D7×#1652, … |
| maximal quotient of | D7×#2347, D7×#2354, D7×#2355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18837);