Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25×C4 |
| direct product | C61×#25808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×C61×#577 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G | |
1424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 97 points:
(2,4)(5,6,11,17)(7,18,8,13)(9,24,26,32)(10,16,22,15)(12,21,28,20)(14,30,33,25)(19,34,23,27)(29,35,31,36)(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);(5,7,10,20,11,8,22,21)(6,12,15,18,17,28,16,13)(9,19,25,35,26,23,30,36)(14,27,24,31,33,34,32,29);(1,2,3,4)(5,8)(6,13)(7,11)(9,19)(10,21)(12,15)(14,31)(16,28)(17,18)(20,22)(23,26)(24,34)(25,35)(27,32)(29,33)(30,36);(5,9,10,25,11,26,22,30)(6,14,15,24,17,33,16,32)(7,19,20,35,8,23,21,36)(12,27,18,31,28,34,13,29)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 18796);