Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C25 |
| direct product | C4×C61×#401 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C61 | C23 |
| commutator | C23 | C23×C4×C61 |
| Frattini, cosocle | C24 | C24×C61 |
| socle, prime radical | C24×C61 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C61 ◁ G | |
1222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,3,4)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(5,6,9,11)(7,12,8,10)(13,14,16,18)(15,17,19,20)(21,22)(23,25)(24,26)(27,28);(5,7,9,8)(6,10,11,12)(13,15,16,19)(14,17,18,20)(21,23,24,27)(22,25,26,28);(5,8,9,7)(6,10,11,12)(14,18)(17,20)(22,26)(23,27)5368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6854);