Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C29 |
| direct product | C61×#61100 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| socle | C2×C61 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ G | |
2616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,13)(4,15)(5,9)(6,10)(7,11)(8,12)(14,29)(16,18)(17,30)(19,23)(20,32)(21,26)(22,28)(24,27)(25,31)(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)(2,4)(5,20)(6,15)(7,23)(8,16)(9,25)(10,18)(11,13)(12,19)(14,21)(17,27)(22,30)(24,31)(26,32)(28,29);(1,4)(2,3)(5,17)(6,18)(7,13)(8,19)(9,14)(10,15)(11,23)(12,16)(20,27)(21,25)(22,32)(24,29)(26,30)(28,31);(1,5)(2,9)(3,14)(4,17)(6,21)(7,24)(8,22)(10,26)(11,27)(12,28)(13,29)(15,30)(16,31)(18,25)(19,32)(20,23);(1,6,8,7)(2,10,12,11)(3,15,16,23)(4,18,19,13)(5,21,22,24)(9,26,28,27)(14,30,31,20)(17,25,32,29)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 54088);