Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#11099 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #117 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C22×C59 | #380 |
| prime radical | C22×#41×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×M16×C59 ◁ G | |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(5,6,10,14,11,15,9,24)(7,16,19,27,20,31,18,12)(8,21,22,28,23,13,25,29)(17,32,33,36,34,30,35,26)(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);(1,2)(3,4)(5,7,9,18,11,20,10,19)(6,12,14,16,15,27,24,31)(8,17,22,33,23,34,25,35)(13,26,28,30,21,36,29,32);(2,4)(5,8)(6,13)(7,17)(9,22)(10,25)(11,23)(12,26)(14,28)(15,21)(16,30)(18,33)(19,35)(20,34)(24,29)(27,36)(31,32)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4087);