Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#10376 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C61 |
| prime radical | C2×#121×C61 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,3,5)(4,6,8,7)(9,10)(11,17,19,23)(12,15)(13,16)(14,20,18,21)(22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(2,5)(6,7)(9,10)(11,18,19,14)(12,15)(13,16)(17,20,23,21)(22,24);(2,6)(4,8)(5,7)(9,11)(10,14)(12,21)(13,19)(15,23)(16,18)(17,24)(20,22)2257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3364);