Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#12586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#99 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C22×Q8 | C23×C59 |
| prime radical | C24×C59 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C24×C59 ◁ C23×Q8×C59 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(5,6,9,13,10,14,24,30)(7,15,18,32,16,31,22,35)(8,19,20,29,21,12,23,28)(11,25,27,33,26,34,36,17)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,2,3,4)(5,7)(6,11,14,26)(8,17)(9,22)(10,16)(12,15,19,31)(13,27,30,36)(18,24)(20,34)(21,33)(23,25)(28,32,29,35);(7,16)(11,26)(15,31)(17,33)(18,22)(25,34)(27,36)(32,35)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 5574);