Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C27 |
| direct product | C61×#23412 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C2×C61 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
1948 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)(3,13)(4,18)(5,10)(6,11)(7,12)(8,16)(9,19)(14,22)(15,23)(17,27)(20,26)(21,25)(24,30)(28,29)(31,32)(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)(4,14)(5,15)(6,16)(7,17)(9,24)(10,13)(11,27)(12,23)(18,28)(19,29)(20,31)(21,30)(22,26)(25,32);(1,4)(2,9)(3,14)(5,19)(6,20)(7,21)(8,22)(10,25)(11,18)(12,26)(13,28)(15,29)(16,31)(17,30)(23,24)(27,32);(1,5,7,6)(2,10,12,11)(3,15,17,16)(4,19,21,20)(8,13,23,27)(9,25,26,18)(14,29,30,31)(22,28,24,32)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 16400);