Finite Group DatabasebetaFinite Group Databasebeta| order | 760 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×C22⋊D5 |
| unambiguous semidirect product | C22⋊(D5×C19) |
| Fitting | C22×C5×C19 ⋊ C2 |
| Hall | C5×C19 ⋊ D4 |
| Sylow | C5 ⋊ D4×C19 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C19 | C2×D5 |
| commutator, cosocle | C2×C5 | C22×C19 |
| Frattini | C2 | C2×D5×C19 |
| Fitting | C22×C5×C19 | C2 |
| socle | C2×C5×C19 | C22 |
| hypercenter | C22×C19 | D5 |
| hypocenter | C5 | D4×C19 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C19 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 380 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,24,22)(26,28);(21,22)(23,24)(25,26)(27,28)247 conjugacy classes — view the full character table.
| maximal subgroup of | #13095141, #13095143, D19×C22⋊D5, … |
| maximal normal subgroup of | #13095141, #13095143, D19×C22⋊D5, … |
| maximal quotient of | C19×#683, C19×#685, C19×#686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(760, 23);