Finite Group DatabasebetaFinite Group Databasebeta| order | 21875 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C252 · Schur multiplier (H2) = C53 |
| direct product | C7×#15691059 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C53×C7 | C52 |
| commutator | C5 | C7×C252 |
| Frattini, cosocle | C53 | C52×C7 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C53×C7 ◁ G | |
322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 21875 |
A minimal faithful permutation representation — 2 generators on 82 points:
(1,2,4,8,15)(3,6,10,17,22)(5,11,20,25,21)(7,13,19,16,23)(9,18,24,14,12)(26,27,29,32,36,28,30,33,37,41,31,34,38,42,45,35,39,43,46,48,40,44,47,49,50)(76,77,78,79,80,81,82);(2,5,12,13,6)(4,9,10,11,19)(8,16,20,17,18)(15,22,23,24,25)(51,52,54,57,61,53,55,58,62,66,56,59,63,67,70,60,64,68,71,73,65,69,72,74,75)5075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21875, 2);