Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C59 · Schur multiplier (H2) = C4 |
| direct product | C59×#7197 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #95 |
| commutator | C23 | C4×C8×C59 |
| Frattini, cosocle | C2×C4×C8 | C22×C59 |
| socle | C22×C59 | #336 |
| prime radical | C23×C59 | C4×C8 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C4×C8×C59 ◁ G | |
184 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 2 generators on 107 points:
(1,2)(3,9,10,6)(4,8)(5,7)(11,15,16,13)(12,14)(17,18,20,24,21,26,31,38,22,25,32,37,33,39,44,47)(19,27,29,40,30,41,43,48,28,23,34,35,42,36,45,46)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3,4,11,5,10,12,16)(2,6,8,13,7,9,14,15)(17,19)(18,23,25,27)(20,29)(21,30)(22,28)(24,35,37,40)(26,36,39,41)(31,43)(32,34)(33,42)(38,46,47,48)(44,45)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 185);