Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C25 |
| direct product | C4×C61×#473 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #121 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C22×C61 | C2×#121 |
| prime radical | C2×#41×C61 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G | |
882 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 97 points:
(1,2,3,4)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(5,6,11,16)(7,17,21,27)(8,22,24,30)(9,15,10,14)(12,20,28,19)(13,25,29,23)(18,32,34,26)(31,35,36,33);(5,7,10,20,11,21,9,19)(6,12,15,27,16,28,14,17)(8,18,25,35,24,34,23,33)(13,26,30,36,29,32,22,31);(5,8)(6,13)(7,18)(9,23)(10,25)(11,24)(12,26)(14,22)(15,30)(16,29)(17,31)(19,33)(20,35)(21,34)(27,36)(28,32)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 14542);