Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#33848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C4×D4×C61 ◁ C8×D4×C61 ◁ G | |
696 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)(5,6,10,14)(7,15,19,34)(8,20,23,33)(9,24,22,12)(11,26,28,17)(13,30,32,21)(16,29,35,27)(18,36,25,31)(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)(6,11,14,28)(8,16,23,35)(9,25,22,18)(12,29,24,27)(13,31,32,36)(15,33,34,20)(17,30,26,21);(2,4);(6,12)(7,16)(8,21)(9,22)(11,15)(13,32)(14,24)(17,18)(19,35)(23,30)(25,26)(27,36)(28,34)(29,31)3355 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26836);