Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#24287 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C2×C61 | #2408 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,15)(4,19)(5,23)(6,13)(7,12)(8,14)(9,17)(10,21)(11,20)(16,27)(18,32)(22,28)(24,31)(25,29)(26,30)(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);(1,3,6,17,8,18,7,25)(2,9,12,15,14,29,13,32)(4,20,21,24,22,16,26,5)(10,27,19,31,30,11,28,23);(1,4)(2,10)(3,16)(5,17)(6,21)(7,26)(8,22)(9,27)(11,29)(12,19)(13,28)(14,30)(15,31)(18,20)(23,32)(24,25);(1,5,6,20,8,24,7,16)(2,11,12,23,14,27,13,31)(3,4,17,21,18,22,25,26)(9,28,15,10,29,19,32,30)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 17275);