Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C59 · Schur multiplier (H2) = C22 |
| direct product | C2×C59×M128 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C59 | C22 |
| commutator | C2 | C22×C32×C59 |
| Frattini, cosocle | C32 | C23×C59 |
| socle | C22×C59 | C2×C32 |
| prime radical | C23×C59 | C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C59 ◁ G | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 125 points:
(1,2)(67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125);(3,4,5,11,6,12,15,29,7,13,16,30,19,32,35,51,8,14,17,31,20,33,36,52,22,34,38,53,41,54,55,64,9,10,18,25,21,26,37,45,23,27,39,46,42,48,56,60,24,28,40,47,43,49,57,61,44,50,58,62,59,63,65,66);(4,10)(11,25)(12,26)(13,27)(14,28)(29,45)(30,46)(31,47)(32,48)(33,49)(34,50)(51,60)(52,61)(53,62)(54,63)(64,66)9440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6724);