Finite Group DatabasebetaFinite Group Databasebeta| order | 776 |
| isoclinism | isoclinic class of D97 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D97 |
| Fitting | C4×C97 ⋊ C2 |
| derived, Sylow | C97 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D97 |
| commutator, hypocenter | C97 | C2×C4 |
| Frattini | C2 | C2×D97 |
| Fitting | C4×C97 | C2 |
| socle, cosocle | C2×C97 | C22 |
| prime radical | C2×D97 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 388 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D97, #13095494, C2×C4×D97, … |
| maximal normal subgroup of | C8×D97, #13095494, C2×C4×D97, … |
| maximal quotient of | C4×Dic97, #13095488, #13095490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(776, 5);