Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #2263 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C2×C61×#2263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C24×C61 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C22×C8×C61 ◁ C22×C16×C61 ◁ G | |
502 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(3,4)(5,9)(6,18)(7,21)(8,10)(11,14)(12,15)(13,19)(16,28)(17,22)(20,34)(23,30)(24,29)(25,31)(26,32)(27,33);(4,9)(5,14)(6,15)(7,19)(10,22)(11,12)(13,28)(16,33)(17,31)(18,23)(20,32)(21,24)(25,26)(27,34)(29,30);(4,10)(9,22)(11,25)(12,26)(13,21)(18,34)(23,27)(24,28)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26967);