Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C27 |
| direct product | C61×#23414 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C2×C61 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
1980 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)(3,11)(4,8)(5,17)(6,10)(7,13)(9,19)(12,27)(14,25)(15,23)(16,31)(18,21)(20,32)(22,29)(24,30)(26,28)(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)(2,7)(4,12)(5,18)(6,14)(8,22)(9,25)(10,21)(11,17)(13,19)(15,28)(16,32)(20,23)(24,26)(27,31)(29,30);(1,4)(2,8)(3,12)(5,16)(6,15)(7,20)(9,24)(10,23)(11,26)(13,29)(14,28)(17,31)(18,32)(19,30)(21,22)(25,27);(4,15)(8,23)(12,28)(16,30)(20,22)(24,31)(26,27)(29,32)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 16402);