Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#13127 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #388 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C2×C59 | #1924 |
| prime radical | C2×#41×C59 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×C8×C59 ◁ G | |
300 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,6,12,5,10,14,9,7,11,23,29,21,30,4,19)(3,13,15,28,17,8,20,26,18,27,22,31,16,25,32,24)(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);(1,3,14,32,21,16,6,22,7,18,4,20,5,17,23,15)(2,8,9,28,30,13,12,24,11,25,19,31,10,27,29,26);(1,4,5,6,7,14,21,23)(2,9,10,29,11,19,30,12)(3,15,16,32,18,22,17,20)(8,24,13,31,25,26,27,28)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6115);