Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#11132 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #397 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C23×C4 | C23×C61 |
| socle | C2×C61 | #1439 |
| prime radical | C22×#41×C61 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
864 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,12)(4,17,21,9)(5,22)(6,10)(7,11)(8,14)(13,28,31,25)(15,29)(16,24)(18,23,30,32)(19,26,20,27)(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);(1,3,5,14,7,15,6,16)(2,8,10,12,11,24,22,29)(4,18,19,13,21,30,20,31)(9,25,26,32,17,28,27,23);(1,4)(2,9)(3,13)(5,20)(6,19)(7,21)(8,23)(10,27)(11,17)(12,28)(14,18)(15,31)(16,30)(22,26)(24,32)(25,29)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4120);