Finite Group DatabasebetaFinite Group Databasebeta| order | 616 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D28 |
| unambiguous semidirect product | C4⋊(C11×D7) |
| Fitting | C4×C7×C11 ⋊ C2 |
| Hall | C7×C11 ⋊ D4 |
| Sylow | C7 ⋊ D4×C11 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11 | C2×D7 |
| commutator, cosocle | C2×C7 | C22×C11 |
| Frattini | C2 | C2×C11×D7 |
| Fitting | C4×C7×C11 | C2 |
| socle | C2×C7×C11 | C22 |
| hypercenter | C4×C11 | D7 |
| hypocenter | C7 | D4×C11 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C11 ◁ C4×C11 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 308 |
187 conjugacy classes — view the full character table.
| maximal subgroup of | #11927628, #11927630, #11927632, … |
| maximal normal subgroup of | #11927628, #11927630, #11927632, … |
| maximal quotient of | C11×#1132, C11×D56, C11×Dic28, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(616, 19);