Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#24229 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C61×#3497 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
1330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 97 points:
(2,3)(5,6)(7,11)(8,18)(9,21)(10,14)(12,20)(13,24)(15,32)(16,30)(17,27)(19,31)(22,26)(23,29)(25,34)(28,35)(33,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(1,2,4,3)(5,7,10,17)(6,11,14,27)(8,15,19,33)(9,22,24,16)(12,28,29,25)(13,30,21,26)(18,32,31,36)(20,35,23,34);(5,8,10,19)(6,12,14,29)(7,15,17,33)(9,23,24,20)(11,25,27,28)(13,31,21,18)(16,35,22,34)(26,36,30,32);(1,3,4,2)(8,19)(12,29)(15,33)(18,31)(20,23)(25,28)(32,36)(34,35)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 17217);