Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C59×#18386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#1595 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
984 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)(4,16)(8,22)(9,20)(10,17)(12,26)(13,29)(14,15)(18,31)(21,28)(23,27)(24,32)(25,30)(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)(3,12)(4,17)(5,10)(6,9)(7,16)(8,14)(11,23)(13,21)(15,28)(18,32)(19,24)(20,31)(22,25)(26,29)(27,30);(4,18)(7,20)(13,29)(16,31)(17,32)(21,26)(22,27)(25,30);(1,3,6,15)(2,8,9,23)(4,13,18,29)(5,14,19,11)(7,21,20,26)(10,12,24,28)(16,30,31,25)(17,27,32,22)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11374);