Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11234 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #391 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C2×C59 | #1441 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G | |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2)(3,12)(4,16,19,31)(5,20)(6,10)(7,11)(8,14)(9,18,26,17)(13,22,29,25)(15,23)(21,24)(27,28,30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,5,14,7,15,6,21)(2,8,10,12,11,24,20,23)(4,13,17,28,19,29,18,32)(9,25,16,30,26,22,31,27);(1,4,5,17,7,19,6,18)(2,9,10,16,11,26,20,31)(3,13,14,28,15,29,21,32)(8,22,12,27,24,25,23,30)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4222);