Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D7×#557 |
| Fitting | C7×#557 ⋊ C2 |
| Sylow | C7 ⋊ C2×#557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×#557 | C2 |
| prime radical | C22×D7 | C24 |
| hypercenter | #557 | D7 |
| hypocenter | C7 | C2×#557 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1048 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1626, D7×#1636, D7×#1648, … |
| maximal normal subgroup of | D7×#1626, D7×#1636, D7×#1648, … |
| maximal quotient of | Q8×D7×C4⋊C4, D7×#2351, D7×#2355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18864);