Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | D7×#388 |
| Fitting | C7×#388 ⋊ C2 |
| Sylow | C7 ⋊ C2×#388 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C7×#388 | C2 |
| socle, cosocle | C23×C7 | C24 |
| prime radical | C24×D7 | C22 |
| hypercenter | #388 | D7 |
| hypocenter | C7 | C2×#388 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #388 | |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D7×#388, D7×#2290, D7×#2293, … |
| maximal normal subgroup of | C2×D7×#388, D7×#2290, D7×#2293, … |
| maximal quotient of | D7×#1434, D7×#1436, D7×#1437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 8035);