Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13316 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#13317 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C59×#3054 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C22×M16×C59 ◁ G | |
552 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)(7,15)(8,19)(9,24)(10,13)(11,16)(12,23)(14,22)(17,35)(18,32)(20,30)(21,31)(25,28)(26,34)(27,36)(29,33)(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);(5,7,10,18)(6,11,13,26)(8,20,21,36)(9,25,22,17)(12,28,29,35)(14,30,24,27)(15,31,32,19)(16,33,34,23);(2,4)(8,21)(11,26)(12,29)(16,34)(19,31)(20,36)(23,33)(27,30)2006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6305);