Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C61 · Schur multiplier (H2) = C214 |
| direct product | C61×#63090 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C26×C61 |
| socle | C2×C61 | C24×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×#41×C61 ◁ G | |
10836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 6 generators on 93 points:
(1,2)(3,12)(4,9)(5,11)(6,19)(7,10)(8,14)(13,26)(15,23)(16,24)(17,25)(18,29)(20,22)(21,28)(27,32)(30,31)(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)(2,8)(4,13)(5,14)(6,20)(7,15)(9,21)(10,22)(11,23)(12,19)(16,27)(17,28)(18,30)(24,31)(25,32)(26,29);(1,4)(2,9)(3,13)(5,17)(6,18)(7,16)(8,21)(10,24)(11,25)(12,26)(14,28)(15,27)(19,29)(20,30)(22,31)(23,32);(4,16)(9,24)(13,27)(17,18)(21,31)(25,29)(26,32)(28,30);(2,10)(8,22)(9,24)(11,19)(12,23)(21,31)(25,29)(26,32);(1,5,7,6)(2,11,10,19)(3,14,15,20)(4,17,16,18)(8,23,22,12)(9,25,24,29)(13,28,27,30)(21,32,31,26)5002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 56078);