Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#29882 |
| 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 | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 97 points:
(5,6)(7,11)(8,12)(9,10)(13,19)(14,17)(15,20)(16,18)(21,22,26,30,25,29,34,36)(23,31,32,28,24,27,33,35)(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);(1,2)(3,4)(6,10)(11,17)(12,18)(19,20)(21,23)(22,27)(24,25)(26,32)(28,36)(29,31)(30,35)(33,34);(2,4)(5,7,9,14)(6,11,10,17)(8,15,16,13)(12,20,18,19)(21,24,25,23)(22,28,29,35)(26,32,34,33)(27,30,31,36);(5,8,9,16)(6,12,10,18)(7,13,14,15)(11,19,17,20)(23,24)(27,31)(28,35)(32,33)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22870);