Finite Group DatabasebetaFinite Group Databasebeta| order | 18870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C17⋊(D37⋊C3)) |
| unambiguous semidirect product | C17⋊(C5⋊(D37⋊C3)) |
| unambiguous semidirect product | (C37⋊C3)⋊D85 |
| unambiguous semidirect product | D3145⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C37 | C2×C3 |
| LCS | G ▷ C5×C17×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 3145 |
A minimal faithful permutation representation — 2 generators on 59 points:
(2,6,7,3,4,8)(5,14,15,9,10,23)(11,26,27,17,18,34)(12,25,21,19,16,13)(20,36,37,29,28,32)(22,24,35,31,30,33)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(56,57)(58,59);(1,2,5,11,18,28,33,34,31,21,7,6,12,20,30,10,16,23,32,37,15,25,14,24,29,19,4,8,13,22,27,35,36,26,17,9,3)(38,39,41,43,45,47,49,51,53,54,52,50,48,46,44,42,40)(55,56,58,59,57)Polycyclic presentation:
2,3,5,17,37|c^a=c^4,d^a=d^16,e^a=e^36,e^b=e^26642 conjugacy classes — view the full character table.
| maximal subgroup of | #27160370⋊C3, #27160371⋊C3, #27160374⋊C3, … |
| maximal normal subgroup of | #27160370⋊C3, #27160371⋊C3, #27160374⋊C3, … |
| maximal quotient of | Dic3145⋊C3, C2×C5⋊(C17⋊(D37⋊C3)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18870, 24);