Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19651 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23×C4 |
| direct product | C61×#19659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C61×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
700 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,9)(4,6)(5,13)(7,11)(8,12)(10,15)(14,16)(17,18,22,25)(19,26,24,21)(20,28,29,27)(23,31,32,30)(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);(2,6)(7,14)(8,13)(9,15)(17,19,21,18,22,24,26,25)(20,27,30,23,29,28,31,32);(1,3,5,11,4,10,12,16)(2,7,8,9,6,14,13,15)(17,20,21,30,22,29,26,31)(18,23,24,28,25,32,19,27);(20,29)(23,32)(27,28)(30,31)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12647);