Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#33337 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C61 |
| Frattini, cosocle | C2×C8 | C24×C61 |
| socle | C2×C61 | C22×C22⋊C8 |
| prime radical | C22×#41×C61 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C2×#131×C61 ◁ G | |
1128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,9,5,10,15,22,6,7,14,18,16,19,26,29)(3,8,12,20,13,21,25,30,11,17,23,27,24,28,31,32)(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);(2,7)(4,14)(8,17)(10,19)(12,23)(15,26)(21,28)(25,31);(1,3)(2,8)(4,12)(5,13)(6,11)(7,17)(9,20)(10,21)(14,23)(15,25)(16,24)(18,27)(19,28)(22,30)(26,31)(29,32);(3,11)(8,17)(12,23)(13,24)(20,27)(21,28)(25,31)(30,32)5002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26325);