Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C2×C59×#3314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| prime radical | C2×C59×#546 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G | |
2298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 85 points:
(1,2)(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);(3,4,6,8)(5,9,10,7)(11,12,15,19)(13,16,20,24)(14,17,22,18)(21,25,26,23);(3,5)(4,7)(6,10)(8,9)(11,13)(12,16)(14,21)(15,20)(17,25)(18,23)(19,24)(22,26);(12,17)(13,20)(14,22)(16,23)(18,19)(24,25);(5,10)(7,9)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 54114);