Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#18263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C61×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
948 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,6,4)(3,11,15,27)(5,18,20,30)(7,9,22,16)(8,23,12,13)(10,25,17,21)(14,26,29,31)(19,24,32,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,7,14)(2,8,9,24)(4,12,16,28)(5,19,21,13)(6,15,22,29)(10,26,18,11)(17,31,30,27)(20,32,25,23);(1,4)(2,6)(3,12)(5,10)(7,16)(8,15)(9,22)(11,13)(14,28)(17,20)(18,21)(19,26)(23,27)(24,29)(25,30)(31,32);(2,9)(4,16)(8,24)(10,18)(11,26)(12,28)(17,30)(27,31)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 11251);