Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D7×#541 |
| Fitting | C7×#541 ⋊ C2 |
| Sylow | C7 ⋊ C2×#541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×#541 | C2 |
| prime radical | C23×D7 | C23 |
| hypercenter | #541 | D7 |
| hypocenter | C7 | C2×#541 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #541 | |
1004 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3120, D7×#3123, D7×#3127, … |
| maximal normal subgroup of | D7×#3120, D7×#3123, D7×#3127, … |
| maximal quotient of | D7×#2314, D7×#2320, D7×#2323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18342);