Finite Group DatabasebetaFinite Group Databasebeta| order | 11130 |
| automorphism | Aut(G) order 13890240 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5565 |
| unambiguous semidirect product | C3⋊D1855 |
| unambiguous semidirect product | C5⋊D1113 |
| unambiguous semidirect product | C7⋊D795 |
| unambiguous semidirect product | C53⋊D105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C53 | C2 |
| LCS | G ▷ C3×C5×C7×C53 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 68 |
| transitive degree | μt(G) = 5565 |
A minimal faithful permutation representation — 2 generators on 68 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68);(2,3)(5,8)(6,7)(10,15)(11,14)(12,13)(17,68)(18,67)(19,66)(20,65)(21,64)(22,63)(23,62)(24,61)(25,60)(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)Polycyclic presentation:
2,3,5,7,53|b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^522784 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×D105, D7×D795, D15×D371, … |
| maximal normal subgroup of | D53×D105, D7×D795, D15×D371, … |
| maximal quotient of | Dic5565, C2×D5565, D16695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11130, 17);