Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#17623 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#3505 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C4×D4×C59 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,8,11,25)(3,14)(5,18)(9,27,28,30)(10,24,23,29)(12,26,13,21)(15,31)(17,19)(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);(1,2)(3,9)(4,10)(5,21)(6,12)(7,13)(8,15)(11,22)(14,24)(16,30)(17,29)(18,25)(19,28)(20,27)(23,32)(26,31);(1,3)(2,9)(4,18)(5,16)(6,14)(7,17)(8,23)(10,25)(11,28)(12,24)(13,29)(15,32)(19,22)(20,31)(21,30)(26,27);(1,4,6,16)(2,10,12,30)(3,15,14,31)(5,19,18,17)(7,20,22,32)(8,24,26,9)(11,23,13,27)(21,28,25,29)2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10611);