Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#33351 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C22×#99 |
| commutator | C23 | C23×C4×C61 |
| Frattini, cosocle | C2×D4 | C24×C61 |
| prime radical | C61×#3487 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×Q8×C61 ◁ C2×2−1+4×C61 ◁ G | |
1212 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)(4,9)(5,10)(6,20,21,11)(7,12)(8,15,23,19)(14,24)(16,29,30,25)(17,26)(18,27)(22,28,32,31)(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);(1,3,7,5)(2,8,12,23)(4,14,17,18)(6,15,21,19)(9,22,26,32)(10,11,13,20)(16,28,30,31)(24,29,27,25);(1,4,7,17)(2,9,12,26)(3,14,5,18)(6,16,21,30)(8,22,23,32)(10,27,13,24)(11,25,20,29)(15,28,19,31);(1,5,7,3)(2,10,12,13)(4,14,17,18)(6,19,21,15)(8,11,23,20)(9,24,26,27)(16,28,30,31)(22,29,32,25)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26339);