Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11236 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #124 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C22×C59 | #394 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2,3,4)(5,6)(7,17)(8,21)(9,15)(10,14)(11,16)(12,19)(13,23)(18,28)(20,31)(22,30)(24,29)(25,27)(26,34)(32,33)(35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(5,7,9,19,11,20,10,25)(6,12,14,17,16,27,15,31)(8,18,22,33,24,34,23,35)(13,28,29,36,30,26,21,32);(5,8,9,22,11,24,10,23)(6,13,14,29,16,30,15,21)(7,18,19,33,20,34,25,35)(12,26,17,32,27,28,31,36)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4224);