Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#11059 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #386 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| prime radical | C24×C59 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,4)(5,6,10,16,11,14,9,15)(7,12,18,28,19,27,25,32)(8,20,23,30,24,13,22,31)(17,33,21,36,34,26,35,29)(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)(6,12)(8,21)(9,25)(10,18)(11,19)(13,29)(14,27)(15,32)(16,28)(17,22)(20,36)(23,34)(24,35)(26,30)(31,33);(5,8,11,24)(6,13,14,20)(7,17,19,34)(9,23,10,22)(12,26,27,33)(15,31,16,30)(18,35,25,21)(28,36,32,29)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4047);