Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C27 |
| direct product | C61×#20998 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #386 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C2×C61 | C2×#386 |
| prime radical | C2×C61×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
1704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,6,11,7,12,5,10)(3,13,16,24,17,23,15,8)(4,18,19,9,21,25,20,26)(14,22,28,31,30,32,29,27)(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)(2,8,12,24)(4,14)(5,15)(6,16)(7,17)(9,22,26,32)(10,23,11,13)(18,27,25,31)(19,28)(20,29)(21,30);(1,4)(2,9)(3,14)(5,19)(6,20)(7,21)(8,22)(10,25)(11,18)(12,26)(13,27)(15,28)(16,29)(17,30)(23,31)(24,32);(1,5,7,6)(2,10,12,11)(3,15,17,16)(4,19,21,20)(8,23,24,13)(9,25,26,18)(14,28,30,29)(22,31,32,27)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 13986);