Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#23456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C23×D4×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×#117×C59 ◁ G | |
1362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 87 points:
(5,6,8,10)(7,11,12,9)(13,14)(15,18)(16,19)(17,21)(20,24)(22,26)(23,25)(27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(1,2)(3,4)(5,7,8,12)(6,9,10,11)(13,15)(14,18)(16,23)(17,22)(19,25)(20,27)(21,26)(24,28);(2,4)(14,19)(16,24)(18,25)(20,21)(23,28)(26,27);(15,22)(18,26)(23,28)(25,27)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16444);