Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13310 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#13310 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,14)(4,8)(5,13)(6,11)(7,12)(9,16)(10,18)(15,29)(17,28)(19,24)(20,23)(21,27)(22,30)(25,32)(26,31)(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);(2,8)(4,18)(5,6)(9,25)(10,13)(11,24)(12,23)(14,29)(15,30)(16,21)(19,20)(22,27)(26,28)(31,32);(1,3)(2,9)(4,15)(5,21)(6,16)(7,17)(8,22)(10,26)(11,28)(12,27)(13,14)(18,30)(19,32)(20,31)(23,25)(24,29)2074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6298);