Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C61×#3216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| prime radical | C2×C61×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G | |
2166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 5 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)(5,9)(6,8)(7,10)(11,12,16,19)(13,20,21,26)(14,18,15,23)(17,24,25,22);(3,5,6,10)(4,7,8,9)(13,21)(17,25)(20,26)(22,24);(5,10)(7,9)(11,13)(12,17)(14,22)(15,24)(16,21)(18,26)(19,25)(20,23);(4,8)(7,9)(11,14,16,15)(12,18,19,23)(13,22,21,24)(17,26,25,20)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 53776);