Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×C7⋊#564 |
| unambiguous semidirect product | (C2×C7)⋊#564 |
| Sylow | C7 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D7 |
| commutator, cosocle | C22×C7 | C25 |
| Frattini | C22 | C24×D7 |
| Fitting | C2×C7×#125 | C2 |
| socle, prime radical | C23×C7 | C24 |
| hypercenter | C2×#125 | D7 |
| hypocenter | C7 | C2×#564 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
896 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | #13246250, #13246251, C2×#11729004, … |
| maximal normal subgroup of | #13246250, #13246251, C2×#11729004, … |
| maximal quotient of | C2×#11733438, C2×#11732423, C2×#11732424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17922);