Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | D7×#392 |
| Fitting | C7×#392 ⋊ C2 |
| Sylow | C7 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#392 | C2 |
| hypercenter | #392 | D7 |
| hypocenter | C7 | C2×#392 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #392 | |
1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1343, #13264450, D7×#1595, … |
| maximal normal subgroup of | D7×#1343, #13264450, D7×#1595, … |
| maximal quotient of | D7×#1438, D7×#1439, D7×#1444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 8963);