Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#25446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #2428 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C4×C61 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,6,10,7,11,5,22)(3,12,16,13,17,26,15,8)(4,18,20,24,21,31,19,9)(14,27,29,32,30,23,28,25)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3)(2,8,11,13)(4,14)(5,15)(6,16)(7,17)(9,23,24,27)(10,12,22,26)(18,25,31,32)(19,28)(20,29)(21,30);(1,2)(3,13)(4,9)(5,10)(6,22)(7,11)(8,17)(12,16)(14,27)(15,26)(18,19)(20,31)(21,24)(23,30)(25,29)(28,32);(1,4,5,19,7,21,6,20)(2,9,10,18,11,24,22,31)(3,14,15,28,17,30,16,29)(8,23,12,25,13,27,26,32)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 18434);