Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×Dic7 |
| unambiguous semidirect product | (C2×C7)⋊C43 |
| derived, Sylow | C7 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D7 |
| commutator, hypocenter | C7 | C2×C43 |
| Frattini | C23 | C23×D7 |
| Fitting | C22×C42×C7 | C2 |
| socle, prime radical | C24×C7 | C23 |
| cosocle | C23×C7 | C24 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C22×C42 | |
1272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11725542, #13243237, Dic7×#336, … |
| maximal normal subgroup of | C2×#11725542, #13243237, Dic7×#336, … |
| maximal quotient of | C43×Dic7, C2×Dic7×#95, C2×C4×C7⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14262);