Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#13506 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,3,4)(5,6)(7,12)(8,10)(9,11)(14,18)(19,26)(20,27)(21,25)(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);(5,7,9,8)(6,10,11,12)(13,14,15,18)(16,19,22,26)(17,25,23,21)(20,28,27,24);(2,4)(5,8,9,7)(6,10,11,12)(14,19)(16,24)(17,23)(18,26)(20,21)(22,28)(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, 6494);