Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C61 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C61×#1307 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | #95 |
| commutator | C23 | C2×C42×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | C24×C61 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(3,4,7,5,6,9,8,10)(11,12)(13,19,20,16)(14,18)(15,17)(21,25,26,23)(22,24);(3,5,8,9,6,10,7,4)(11,13,14,21,15,20,22,26)(12,16,18,23,17,19,24,25)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1105);