Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C29 |
| direct product | C61×#61051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C61×#525 ◁ G | |
2734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 5 generators on 97 points:
(1,2)(3,4)(5,6)(7,15)(8,12)(9,22)(10,13)(11,18)(14,23)(16,29)(17,26)(19,25)(20,33)(21,27)(24,31)(28,34)(30,36)(32,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(5,7)(6,11)(8,16)(9,17)(10,19)(12,24)(13,26)(14,25)(15,22)(18,23)(20,30)(21,32)(27,36)(28,35)(29,33)(31,34);(2,4)(5,8,10,21)(6,12,13,27)(7,16,19,32)(9,20,23,34)(11,24,26,36)(14,28,22,33)(15,29,25,35)(17,30,18,31);(7,17)(9,23)(11,25)(14,22)(15,26)(16,30)(18,19)(20,34)(24,35)(28,33)(29,36)(31,32);(6,13)(11,26)(12,27)(14,22)(15,25)(24,36)(28,33)(29,35)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 54039);