Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Dic7×#125 |
| Sylow | C7 ⋊ C4×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C2×C7×#125 | C2 |
| socle, prime radical, cosocle | C23×C7 | C24 |
| hypercenter | C2×#125 | D7 |
| hypocenter | C7 | C4×#125 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
484 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×#330, #13244724, #13244733, … |
| maximal normal subgroup of | Dic7×#330, #13244724, #13244733, … |
| maximal quotient of | Dic7×#387, Dic7×#389, Dic7×#382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15233);