Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#33814 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C59×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 99 points:
(2,5)(3,7)(9,10,14,19)(11,15,22,30)(12,16,25,32)(13,26,24,18)(17,33,31,23)(20,27,36,39)(21,37,35,29)(28,40,38,34)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2)(3,6)(4,5)(7,8)(9,11,14,22)(10,15,19,30)(12,20,25,36)(13,21,24,35)(16,27,32,39)(17,28,31,38)(18,29,26,37)(23,34,33,40);(2,5)(6,8)(10,16)(12,23)(13,24)(15,27)(17,18)(19,32)(20,34)(21,35)(25,33)(26,31)(28,29)(30,39)(36,40)(37,38);(1,3,4,7)(2,6,5,8)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26802);