Finite Group DatabasebetaFinite Group Databasebeta| order | 19950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C19 | C2×C3 |
| LCS | G ▷ C52×C7×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1995 |
A minimal faithful permutation representation — 2 generators on 41 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(21,22)(23,24)(25,26)(27,28,30)(29,39,35,32,33,41)(31,36,40,37,38,34);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(20,21,23,25,26,24,22)(27,29,34,40,32)(28,31,33,39,37)(30,35,36,38,41)Polycyclic presentation:
2,3,5^2,7,19|c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^18,c^b=cd,d^b=c^2d^3736 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19950, 117);