Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25×C4 |
| direct product | C61×#25750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
1452 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)(5,6,11,15)(7,12,18,29)(8,19,21,32)(9,23,10,14)(13,25,31,22)(16,30,33,36)(17,28,24,27)(20,35,34,26)(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)(6,12)(8,20)(9,17)(10,24)(11,18)(13,30)(14,27)(15,29)(16,22)(19,35)(21,34)(23,28)(25,33)(26,32)(31,36);(5,8,9,22,11,21,10,25)(6,13,14,19,15,31,23,32)(7,16,17,34,18,33,24,20)(12,26,27,30,29,35,28,36);(1,3,4,2)(8,21)(13,31)(16,33)(19,32)(20,34)(22,25)(26,35)(30,36)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 18738);