Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#13396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C61×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(3,12)(4,17)(5,6)(8,22)(9,24)(10,21)(13,25)(14,29)(15,30)(16,18)(19,20)(23,32)(26,31)(27,28)(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);(1,2)(3,13)(4,9)(5,21)(6,10)(7,11)(8,15)(12,28)(14,27)(16,23)(17,24)(18,22)(19,31)(20,26)(25,29)(30,32);(1,3,6,15,7,14,5,16)(2,8,10,27,11,23,21,13)(4,18,17,29,20,30,19,12)(9,25,24,32,26,28,31,22)2074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6384);