Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#20867 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C2×#120 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C2×C61 | C2×#385 |
| prime radical | C22×#41×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
1312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,6,11,7,10,5,21)(3,12,14,8,16,24,15,23)(4,17,19,9,20,26,18,25)(13,28,29,27,30,22,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,6,14,7,16,5,15)(2,8,11,24,10,23,21,12)(4,13,19,29,20,30,18,31)(9,22,26,32,25,28,17,27);(1,4)(2,9)(3,13)(5,18)(6,19)(7,20)(8,22)(10,25)(11,26)(12,27)(14,29)(15,31)(16,30)(17,21)(23,28)(24,32);(2,10)(8,23)(9,25)(11,21)(12,24)(17,26)(22,28)(27,32)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 13855);