Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D7×#568 |
| Fitting | C7×#568 ⋊ C2 |
| Sylow | C7 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D7 |
| commutator, socle | C2×C7 | C24×C4 |
| Fitting | C7×#568 | C2 |
| prime radical | C2×D7×#41 | C2 |
| cosocle | C4×C7 | C25 |
| hypercenter | #568 | D7 |
| hypocenter | C7 | C2×#568 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1858, #13354640, D7×#1861, … |
| maximal normal subgroup of | D7×#1858, #13354640, D7×#1861, … |
| maximal quotient of | D7×#2873, D7×#2875, Dic7×#568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18999);