Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#33369 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C2×#99 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C2×Q8 | C24×C61 |
| socle | C2×C61 | C22×#99 |
| prime radical | C61×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ C22×#41×C61 ◁ G | |
1220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,6,11,7,12,4,9)(3,13,15,30,14,28,21,32)(5,18,17,29,20,10,22,27)(8,23,26,19,24,31,25,16)(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)(4,15)(5,19)(6,21)(7,14)(9,25)(10,28)(11,26)(12,24)(13,18)(16,20)(17,23)(22,31)(27,32)(29,30);(3,14)(8,24)(13,28)(15,21)(16,19)(23,31)(25,26)(30,32);(1,4,7,6)(2,9,12,11)(3,15,14,21)(5,17,20,22)(8,25,24,26)(10,27,18,29)(13,30,28,32)(16,31,19,23)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26357);