Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#33530 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| socle | C2×C59 | C2×#447 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×C4×C59 ◁ C22×M16×C59 ◁ G | |
1132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,12)(4,9)(5,17)(6,21)(7,11)(8,14)(10,20)(13,29)(15,28)(16,27)(18,23)(19,31)(22,26)(24,30)(25,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3)(2,8)(4,13)(5,18)(6,22)(7,15)(9,23)(10,26)(11,24)(12,17)(14,20)(16,30)(19,32)(21,25)(27,29)(28,31);(5,19)(10,27)(12,28)(14,30)(16,20)(17,31)(18,32)(26,29);(1,4,7,6)(2,9,11,21)(3,13,15,22)(5,16,19,20)(8,23,24,25)(10,17,27,31)(12,29,28,26)(14,18,30,32)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26518);