Finite Group DatabasebetaFinite Group Databasebeta| order | 3740 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic55 |
| unambiguous semidirect product | C11⋊(C17×Dic5) |
| derived, Hall | C5×C11 ⋊ C4×C17 |
| Hall | C5×C11×C17 ⋊ C4 |
| Hall | C11×C17 ⋊ Dic5 |
| Hall | C5×C17 ⋊ Dic11 |
| Sylow | C11 ⋊ C17×Dic5 |
| Sylow | C5 ⋊ C17×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D55 |
| commutator, hypocenter | C5×C11 | C4×C17 |
| Frattini | C2 | C17×D55 |
| Fitting, socle, prime radical | C2×C5×C11×C17 | C2 |
| cosocle | C2×C5×C11 | C2×C17 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2×C17 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3740 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37);(18,20,19,21)(23,26)(24,25)(28,37)(29,36)(30,35)(31,34)(32,33)986 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×Dic55, C17×Dic165, C17×Dic275, … |
| maximal normal subgroup of | C3×C17×Dic55, C17×(C11⋊C5)⋊Dic5, C5×C17×Dic55, … |
| maximal quotient of | C3×C17×Dic55, C17×Dic165, C17×Dic275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3740, 11);