Finite Group DatabasebetaFinite Group Databasebeta| order | 11310 |
| automorphism | Aut(G) order 15200640 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5655 |
| unambiguous semidirect product | C3⋊D1885 |
| unambiguous semidirect product | C5⋊D1131 |
| unambiguous semidirect product | C13⋊D435 |
| unambiguous semidirect product | C29⋊D195 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C13×C29 | C2 |
| LCS | G ▷ C3×C5×C13×C29 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 5655 |
A minimal faithful permutation representation — 2 generators on 50 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(2,3)(5,8)(6,7)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)Polycyclic presentation:
2,3,5,13,29|b^a=b^2,c^a=c^4,d^a=d^12,e^a=e^282829 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D195, D13×D435, D15×D377, … |
| maximal normal subgroup of | D29×D195, D13×D435, D15×D377, … |
| maximal quotient of | Dic5655, C2×D5655, D16965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11310, 17);