Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C27 |
| direct product | C61×#20947 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C2×#120 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C2×C61 | C2×#386 |
| prime radical | C61×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
1708 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)(3,11,14,25)(4,15,17,8)(5,10)(6,9)(7,13,22,18)(12,27)(16,26,19,23)(20,24)(21,28)(29,32)(30,31)(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);(1,3,5,18,6,14,20,13)(2,7,10,25,9,22,24,11)(4,12,19,28,17,29,16,30)(8,21,26,32,15,31,23,27);(1,4)(2,8)(3,12)(5,19)(6,17)(7,21)(9,15)(10,26)(11,27)(13,30)(14,29)(16,20)(18,28)(22,31)(23,24)(25,32);(2,9)(7,22)(8,15)(10,24)(11,25)(21,31)(23,26)(27,32)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 13935);