Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C59×#18370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
1024 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,8)(3,5)(4,16)(9,25)(10,23)(11,20)(12,24)(14,29)(15,21)(17,32)(18,31)(19,28)(22,27)(26,30)(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)(3,8)(4,17)(5,20)(6,11)(7,12)(9,19)(10,13)(14,30)(15,24)(16,26)(18,22)(21,23)(25,29)(27,28)(31,32);(1,3,13,21)(2,8,10,23)(4,14,28,29)(5,7,15,6)(9,22,26,32)(11,20,12,24)(16,31,19,18)(17,30,27,25);(1,4,13,28)(2,9,10,26)(3,14,21,29)(5,18,15,31)(6,19,7,16)(8,22,23,32)(11,17,12,27)(20,30,24,25)2006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11358);