Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#13394 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C2×#41×C61 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G | |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 97 points:
(5,6,12,18)(7,19,22,31)(8,23,20,13)(9,17,11,15)(10,26,29,35)(14,32,34,24)(16,25,36,28)(21,33,27,30)(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)(3,4)(5,7)(6,13)(8,9)(10,27)(11,20)(12,22)(14,26)(15,31)(16,33)(17,19)(18,23)(21,29)(24,28)(25,32)(30,36)(34,35);(2,4)(5,8,9,7,12,20,11,22)(6,14,15,30,18,34,17,33)(10,27,25,24,29,21,28,32)(13,16,19,35,23,36,31,26)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6382);