Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#11266 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #388 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C23×C4 | C23×C61 |
| socle | C2×C61 | #1442 |
| prime radical | C24×C61 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,6,10,7,12,5,11)(3,13,15,8,17,24,16,25)(4,18,20,28,21,27,22,9)(14,30,31,26,32,23,19,29)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,5,16,7,17,6,15)(2,8,11,13,12,25,10,24)(4,19,20,14,21,31,22,32)(9,26,18,23,28,29,27,30);(1,4,5,20,7,21,6,22)(2,9,10,27,12,28,11,18)(3,14,15,19,17,32,16,31)(8,23,13,29,25,30,24,26)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4254);