Finite Group DatabasebetaFinite Group Databasebeta| order | 29610 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D14805 |
| unambiguous semidirect product | C5⋊D2961 |
| unambiguous semidirect product | C7⋊D2115 |
| unambiguous semidirect product | C9⋊D1645 |
| unambiguous semidirect product | C47⋊D315 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C7×C9×C47 | C2 |
| Frattini | C3 | D4935 |
| socle | C3×C5×C7×C47 | D3 |
| LCS | G ▷ C5×C7×C9×C47 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 68 |
| transitive degree | μt(G) = 14805 |
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);(2,9)(3,8)(4,7)(5,6)(11,14)(12,13)(16,21)(17,20)(18,19)(23,68)(24,67)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)Polycyclic presentation:
2,3,5,7,47,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^6,e^a=e^46,f^a=f^27404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D14805 |
| maximal normal subgroup of | C2×D14805 |
| maximal quotient of | Dic14805, C2×D14805 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29610, 17);