Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D7×#381 |
| Fitting | C7×#381 ⋊ C2 |
| Sylow | C7 ⋊ C2×#381 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C7×#381 | C2 |
| socle, cosocle | C23×C7 | C24 |
| prime radical | C24×D7 | C22 |
| hypercenter | #381 | D7 |
| hypocenter | C7 | C2×#381 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #381 | |
1144 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1284, #13243522, D7×#1306, … |
| maximal normal subgroup of | D7×#1284, #13243522, D7×#1306, … |
| maximal quotient of | D7×C22⋊#95, D7×#1434, #13275005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 6329);