Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×Dic7 |
| derived, Sylow | C7 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D7 |
| commutator, hypocenter | C7 | C23×C42 |
| Frattini | C22 | C24×D7 |
| Fitting | C24×C4×C7 | C2 |
| socle, prime radical | C25×C7 | C22 |
| cosocle | C22×C7 | C25 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C24×C4 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13241715, #13259013, #13259037, … |
| maximal normal subgroup of | #13241715, #13259013, #13259037, … |
| maximal quotient of | C22×C42×Dic7, C23×C7⋊#95, C22×#89704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19048);