Finite Group DatabasebetaFinite Group Databasebeta| order | 25830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12915 |
| unambiguous semidirect product | C5⋊D2583 |
| unambiguous semidirect product | C7⋊D1845 |
| unambiguous semidirect product | C9⋊D1435 |
| unambiguous semidirect product | C41⋊D315 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C7×C9×C41 | C2 |
| Frattini | C3 | D4305 |
| socle | C3×C5×C7×C41 | D3 |
| LCS | G ▷ C5×C7×C9×C41 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 12915 |
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);(2,9)(3,8)(4,7)(5,6)(11,14)(12,13)(16,21)(17,20)(18,19)(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:
2,3,5,7,41,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^6,e^a=e^40,f^a=f^26459 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D12915 |
| maximal normal subgroup of | C2×D12915 |
| maximal quotient of | Dic12915, C2×D12915 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25830, 19);