Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C210 |
| direct product | C61×#60387 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| socle | C2×C61 | C22×#120 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
4764 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)(3,12)(4,9)(5,11)(6,18)(7,10)(8,14)(13,28)(15,23)(16,25)(17,24)(19,22)(20,26)(21,30)(27,31)(29,32)(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);(1,3)(2,8)(4,13)(5,14)(6,19)(7,15)(9,21)(10,22)(11,23)(12,18)(16,29)(17,31)(20,30)(24,32)(25,28)(26,27);(1,4)(2,9)(3,13)(5,16)(6,20)(7,17)(8,21)(10,24)(11,25)(12,27)(14,29)(15,31)(18,26)(19,30)(22,32)(23,28);(2,10)(8,22)(9,24)(11,18)(12,23)(21,32)(25,26)(27,28);(1,5,7,6)(2,11,10,18)(3,14,15,19)(4,16,17,20)(8,23,22,12)(9,25,24,26)(13,29,31,30)(21,28,32,27)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 53375);