Finite Group DatabasebetaFinite Group Databasebeta| order | 18870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D9435 |
| unambiguous semidirect product | C3⋊D3145 |
| unambiguous semidirect product | C5⋊D1887 |
| unambiguous semidirect product | C17⋊D555 |
| unambiguous semidirect product | C37⋊D255 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C17×C37 | C2 |
| LCS | G ▷ C3×C5×C17×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 9435 |
A minimal faithful permutation representation — 2 generators on 62 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);(2,3)(5,8)(6,7)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(27,62)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)Polycyclic presentation:
2,3,5,17,37|b^a=b^2,c^a=c^4,d^a=d^16,e^a=e^364719 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×D255, D17×D555, D15×D629, … |
| maximal normal subgroup of | D37×D255, D17×D555, D15×D629, … |
| maximal quotient of | Dic9435, C2×D9435, D28305 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18870, 17);