Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#24290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G | |
1294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 97 points:
(1,2)(3,4)(5,6)(7,13)(8,21)(9,24)(10,17)(11,16)(12,19)(14,25)(15,22)(18,32)(20,28)(23,27)(26,31)(29,33)(30,36)(34,35)(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);(5,7,10,19,11,8,22,20)(6,12,15,13,16,28,17,21)(9,18,25,33,26,23,36,34)(14,27,24,29,30,32,31,35);(2,4)(5,8)(6,13)(7,11)(9,23)(10,20)(12,17)(14,29)(15,28)(16,21)(18,26)(19,22)(24,32)(25,34)(27,31)(30,35)(33,36);(5,9,22,36,11,26,10,25)(6,14,17,31,16,30,15,24)(7,18,20,34,8,23,19,33)(12,27,21,35,28,32,13,29)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 17278);