Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#24408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C4×C61 ◁ G | |
1364 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)(3,11,13,7)(4,8)(5,10)(6,9)(12,21,30,29)(14,27,18,22)(15,23,31,32)(16,25)(17,24)(19,28)(20,26)(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)(2,7)(4,15)(5,18)(6,13)(8,23)(9,11)(10,27)(12,17)(14,20)(16,31)(19,30)(21,24)(22,26)(25,32)(28,29);(1,4)(2,8)(3,12)(5,19)(6,16)(7,21)(9,25)(10,28)(11,29)(13,30)(14,31)(15,18)(17,20)(22,32)(23,27)(24,26);(1,3)(2,7)(4,12)(5,14)(6,13)(8,21)(9,11)(10,22)(15,17)(16,30)(18,20)(19,31)(23,24)(25,29)(26,27)(28,32)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 17396);