Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#13553 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C61 | C23 |
| commutator | C22 | C22×C16×C61 |
| Frattini, cosocle | C2×C16 | C23×C61 |
| socle | C22×C61 | C22×C16 |
| prime radical | C24×C61 | C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C61 ◁ G | |
330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2)(3,4)(5,6,7,12,8,13,15,24,9,14,16,25,18,26,27,34,10,11,17,21,19,22,28,31,20,23,29,32,30,33,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(2,4);(6,11)(12,21)(13,22)(14,23)(24,31)(25,32)(26,33)(34,36)6832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6541);