Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#25143 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2)(3,4)(5,6,10,15,11,16,9,14)(7,12,19,28,20,29,18,27)(8,21,23,31,24,32,25,13)(17,33,34,30,22,36,35,26)(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);(2,4)(5,7,10,19,11,20,9,18)(6,12,15,28,16,29,14,27)(8,22,23,35,24,17,25,34)(13,30,21,36,31,26,32,33);(5,8,11,24)(6,13,16,31)(7,17,20,22)(9,23,10,25)(12,26,29,30)(14,21,15,32)(18,34,19,35)(27,33,28,36);(2,4)(5,9,11,10)(6,14,16,15)(7,18,20,19)(8,23,24,25)(12,27,29,28)(13,21,31,32)(17,34,22,35)(26,33,30,36)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 18131);