Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #89428 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#89443 |
| Fitting | C2×C7×#95 ⋊ C2 |
| Sylow | C7 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D7 |
| commutator, cosocle | C23×C7 | C24 |
| Frattini | C23 | C23×D7 |
| Fitting | C2×C7×#95 | C2 |
| socle | C24×C7 | C23 |
| hypercenter | C2×#95 | D7 |
| hypocenter | C7 | C2×#392 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | #13248804, #13248819, #13253991, … |
| maximal normal subgroup of | #13248804, #13248819, #13253991, … |
| maximal quotient of | C2×#11727180, C2×#11727181, C2×#11727173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5581);