Finite Group DatabasebetaFinite Group Databasebeta| order | 776 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D97 |
| Fitting | C22×C97 ⋊ C2 |
| Sylow | C97 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D97 |
| commutator, socle, cosocle | C2×C97 | C22 |
| Fitting | C22×C97 | C2 |
| hypercenter | C22 | D97 |
| hypocenter | C97 | D4 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 388 |
Polycyclic presentation:
2^3,97|b^a=bc,d^a=d^96197 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D97, C2×C22⋊D97, #13095510, … |
| maximal normal subgroup of | D4×D97, C2×C22⋊D97, #13095510, … |
| maximal quotient of | #13095488, C22⋊Dic97, #13095490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(776, 8);