Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C61 · Schur multiplier (H2) = C2×C4 |
| direct product | C61×#11406 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C61 | C42 |
| commutator | C4 | C2×C4×C8×C61 |
| Frattini, cosocle | C4×C8 | C23×C61 |
| socle | C22×C61 | C2×#97 |
| prime radical | C23×C61 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C61 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 101 points:
(9,10,12,17,13,18,24,33,14,16,25,30,26,31,39,40)(11,19,21,34,22,29,37,32,20,35,23,38,36,15,27,28)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,2,3,5,4,6,7,8)(9,11)(10,15,16,29)(12,23)(13,22)(14,20)(17,32,30,28)(18,19,31,35)(21,25)(24,27)(26,36)(33,38,40,34)(37,39);(10,16)(11,20)(17,30)(18,31)(21,23)(22,36)(27,37)(33,40)5368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4394);