Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24×C4 |
| direct product | C61×#25609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C24×C61 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G | |
1052 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 105 points:
(5,6)(7,11)(8,9)(10,12)(13,14,18,22)(15,19,24,32)(16,26,29,41)(17,30,27,21)(20,34,35,28)(23,36,38,44)(25,40,37,33)(31,42,43,39)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,2)(3,4)(6,9)(10,11)(13,15)(14,19)(16,23)(17,25)(18,24)(20,31)(21,33)(22,32)(26,36)(27,37)(28,39)(29,38)(30,40)(34,42)(35,43)(41,44);(2,4)(13,16,27,34,18,29,17,28)(14,20,30,41,22,35,21,26)(15,23,37,42,24,38,25,39)(19,31,40,44,32,43,33,36);(5,7,8,12)(6,10,9,11)(15,24)(19,32)(23,38)(25,37)(31,43)(33,40)(36,44)(39,42)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 18597);