Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#29888 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×#41×C61 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 109 points:
(1,2)(3,7)(4,8)(5,6)(9,15)(10,13)(11,16)(12,14)(17,18,22,27,21,26,23,28)(19,29,32,44,31,24,38,40)(20,33,36,42,35,43,37,25)(30,46,34,39,47,41,48,45)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(2,6)(7,13)(8,14)(15,16)(17,19)(18,24)(20,34)(21,31)(22,32)(23,38)(25,41)(26,29)(27,40)(28,44)(30,37)(33,45)(35,48)(36,47)(39,43)(42,46);(1,3,5,10)(2,7,6,13)(4,11,12,9)(8,16,14,15)(17,20,21,35)(18,25,26,42)(19,30,31,47)(22,37,23,36)(24,39,29,45)(27,43,28,33)(32,48,38,34)(40,46,44,41);(1,4,5,12)(2,8,6,14)(3,9,10,11)(7,15,13,16)(20,35)(25,42)(30,47)(33,43)(34,48)(36,37)(39,45)(41,46)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22876);