Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C61 · Schur multiplier (H2) = C220 |
| direct product | C61×#63103 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C26 |
| commutator, Frattini, cosocle | C2 | C27×C61 |
| socle | C2×C61 | C27 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ G | |
59452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 7 generators on 93 points:
(1,2)(3,11)(4,8)(5,10)(6,9)(7,13)(12,23)(14,24)(15,20)(16,21)(17,22)(18,25)(19,27)(26,31)(28,30)(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)(2,7)(4,12)(5,14)(6,13)(8,18)(9,11)(10,19)(15,25)(16,26)(17,27)(20,23)(21,29)(22,24)(28,32)(30,31);(1,4)(2,8)(3,12)(5,16)(6,15)(7,18)(9,20)(10,21)(11,23)(13,25)(14,26)(17,28)(19,29)(22,30)(24,31)(27,32);(4,15)(8,20)(12,25)(16,28)(18,23)(21,30)(26,32)(29,31);(3,13)(7,11)(12,25)(14,27)(18,23)(19,24)(26,32)(29,31);(2,9)(7,11)(8,20)(10,22)(18,23)(19,24)(21,30)(29,31);(1,5,6,17)(2,10,9,22)(3,14,13,27)(4,16,15,28)(7,19,11,24)(8,21,20,30)(12,26,25,32)(18,29,23,31)7930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 56091);