Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic112 |
| Sylow | C7 ⋊ C2×Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D112 |
| commutator, cosocle | C7×C16 | C23 |
| Frattini | C16 | C22×D7 |
| Fitting | C2×C7×C32 | C2 |
| socle, prime radical | C22×C7 | D16 |
| hypercenter | C2×C32 | D7 |
| hypocenter | C7 | C2×Q64 |
| LCS | G ▷ C7×C16 ▷ C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | #13241676, #13241678, #13241688, … |
| maximal normal subgroup of | #13241676, #13241678, #13241688, … |
| maximal quotient of | C2×#11725403, C2×#11725397, C4×Dic112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1890);