Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#23814 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C61×#376 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 4 generators on 105 points:
(5,6,8,9)(7,10,11,12)(13,14,17,21,18,22,32,38)(15,23,26,34,25,36,30,19)(16,27,28,35,29,37,31,20)(24,33,41,44,40,43,42,39)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,2)(3,4)(6,9)(10,12)(13,15,18,25)(14,19,22,34)(16,24,29,40)(17,30,32,26)(20,33,35,43)(21,36,38,23)(27,39,37,44)(28,42,31,41);(2,4)(13,16,18,29)(14,20,22,35)(15,24,25,40)(17,31,32,28)(19,33,34,43)(21,37,38,27)(23,39,36,44)(26,42,30,41);(5,7,8,11)(6,10,9,12)(15,25)(19,34)(23,36)(24,40)(26,30)(33,43)(39,44)(41,42)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 16802);