Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#18977 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C61×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,12)(4,9)(5,10)(6,15)(7,11)(8,13)(14,16)(17,18,23,26)(19,29,25,32)(20,30,24,31)(21,28,22,27)(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);(1,3,7,4)(2,8,11,16)(5,13,6,14)(9,15,12,10)(17,19,23,25)(18,24,26,20)(21,31,22,30)(27,32,28,29);(1,4,7,3)(2,9,11,12)(5,13,6,14)(8,15,16,10)(17,20,23,24)(18,25,26,19)(21,29,22,32)(27,30,28,31);(1,5,7,6)(2,10,11,15)(3,13,4,14)(8,9,16,12)(18,26)(20,24)(27,28)(29,32)2257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 11965);