Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C59×#18333 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#392 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,7)(3,11)(4,15)(8,21)(9,19)(10,16)(12,27)(13,14)(17,30)(20,25)(22,28)(23,32)(24,31)(26,29)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2,5,10)(3,8,13,23)(4,16,15,7)(6,9,18,24)(11,25,14,22)(12,28,29,20)(17,31,30,19)(21,26,32,27);(4,17)(7,19)(12,27)(15,30)(16,31)(20,32)(21,28)(26,29);(1,3,6,14)(2,8,9,22)(4,12,17,27)(5,13,18,11)(7,20,19,32)(10,23,24,25)(15,29,30,26)(16,28,31,21)2183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11321);