Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C59 · Schur multiplier (H2) = C2 |
| direct product | C59×#7450 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C59 | #357 |
| commutator | C2×C16 | C2×C4×C59 |
| Frattini, cosocle | C4×C16 | C22×C59 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C42×C59 ◁ C4×C8×C59 ◁ C4×C16×C59 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 2 generators on 99 points:
(2,5)(3,7)(6,8)(9,10,11,16,21,29,36,27,13,18,22,30,25,33,37,28,14,19,23,31,38,40,39,34,24,32,35,26,12,17,20,15)(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);(1,2,4,6)(3,8,7,5)(10,15)(11,20)(12,21)(13,24)(16,17)(18,34)(19,28)(22,39)(23,37)(25,38)(26,29)(27,32)(30,40)(31,33)(35,36)2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 438);