Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D7×Q64 |
| Fitting | C7×Q64 ⋊ C2 |
| Sylow | C7 ⋊ C2×Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D7×D16 |
| commutator, cosocle | C7×C16 | C23 |
| Frattini | C16 | C22×D7 |
| Fitting | C7×Q64 | C2 |
| socle | C2×C7 | C2×D16 |
| prime radical | C2×D7 | D16 |
| hypercenter | Q64 | D7 |
| hypocenter | C7 | C2×Q64 |
| LCS | G ▷ C7×C16 ▷ C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | D7×SD128, D7×Q128, #13274857, … |
| maximal normal subgroup of | D7×SD128, D7×Q128, #13274857, … |
| maximal quotient of | D7×#1416, D7×#1423, #13274379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1902);