Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#33856 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C61×#443 ◁ G | |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,8)(3,13)(4,17)(5,6)(9,10)(11,27)(12,26)(14,30)(15,31)(16,22)(18,23)(20,21)(24,25)(28,29)(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);(1,2)(3,14)(4,18)(5,11)(6,23)(7,12)(8,17)(9,16)(10,15)(13,28)(19,29)(20,26)(21,27)(22,25)(24,32)(30,31);(1,3)(2,9)(4,15)(5,22)(6,13)(7,16)(8,24)(10,27)(11,28)(12,14)(17,19)(18,30)(20,32)(21,31)(23,25)(26,29);(1,3)(2,10)(4,19)(5,13)(6,22)(7,16)(8,25)(9,27)(11,29)(12,30)(14,18)(15,17)(20,31)(21,32)(23,24)(26,28)2623 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26844);