Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C61 · Schur multiplier (H2) = C214 |
| direct product | C2×C61×#3586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C26×C61 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×#41×C61 ◁ G | |
10794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 6 generators on 95 points:
(1,2)(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);(3,4)(5,13)(6,10)(7,19)(8,11)(9,15)(12,21)(14,27)(16,26)(17,24)(18,31)(20,23)(22,29)(25,30)(28,34)(32,33);(3,5,8,16)(4,9,11,23)(6,14,17,28)(7,20,21,15)(10,22,24,33)(12,26,19,13)(18,32,30,29)(25,34,31,27);(3,6)(4,10)(5,14)(7,18)(8,17)(9,22)(11,24)(12,25)(13,27)(15,29)(16,28)(19,31)(20,32)(21,30)(23,33)(26,34);(6,17)(10,24)(14,28)(18,30)(22,33)(25,31)(27,34)(29,32);(4,11)(9,23)(10,24)(12,19)(13,26)(22,33)(25,31)(27,34)5002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 56077);