Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#24286 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C2×C61 | #2408 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ G | |
1322 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)(4,15)(5,18)(6,10)(7,13)(8,17)(9,19)(12,25)(14,23)(16,29)(20,28)(21,26)(22,30)(24,27)(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);(1,3,5,13,6,14,19,28)(2,7,9,11,10,20,18,23)(4,12,17,27,16,26,30,32)(8,21,15,24,22,25,29,31);(4,16)(7,20)(8,22)(11,23)(12,26)(15,29)(17,30)(27,32);(1,4,5,17,6,16,19,30)(2,8,9,15,10,22,18,29)(3,12,13,27,14,26,28,32)(7,21,11,24,20,25,23,31)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 17274);