Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C24×C4 |
| direct product | C61×#21070 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | C22×D4 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C22×C61 | C2×C4×D4 |
| prime radical | C22×#41×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C23×C8×C61 ◁ G | |
1026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 97 points:
(2,3)(5,6,10,15,11,14,9,23)(7,12,18,27,19,26,17,33)(8,20,21,13,22,29,24,28)(16,30,31,25,32,36,34,35)(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);(1,2,4,3)(5,7,10,18,11,19,9,17)(6,12,15,27,14,26,23,33)(8,16,21,31,22,32,24,34)(13,25,29,36,28,35,20,30);(1,3,4,2)(5,8)(6,13)(7,16)(9,24)(10,21)(11,22)(12,25)(14,28)(15,29)(17,34)(18,31)(19,32)(20,23)(26,35)(27,36)(30,33);(6,14)(12,26)(13,28)(15,23)(20,29)(25,35)(27,33)(30,36)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 14058);