Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C2×C59×#1653 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G | |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(4,7)(5,9)(8,10)(11,12,16,20)(13,21,24,25)(14,17,15,19)(18,22,26,23);(3,4,6,8)(5,10,9,7)(12,17)(14,15)(18,25)(19,20)(21,26)(22,23);(11,13,16,24)(12,18,20,26)(14,23,15,22)(17,25,19,21)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11488);