Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#33392 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | C22×#102 |
| commutator | C8 | C23×C4×C59 |
| Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C2×C59×#576 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C2×#41×C59 ◁ C2×#131×C59 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,5,10,6,12,20,11)(3,8,15,25,13,23,28,26)(4,16,18,9,19,7,17,22)(14,29,31,24,27,21,30,32)(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);(2,7)(4,17)(5,20)(8,21)(9,10)(11,22)(12,16)(14,30)(15,28)(18,19)(23,29)(24,25)(26,32)(27,31);(1,3)(2,8)(4,14)(5,15)(6,13)(7,21)(9,24)(10,25)(11,26)(12,23)(16,29)(17,30)(18,31)(19,27)(20,28)(22,32);(3,13)(8,23)(14,27)(15,28)(21,29)(24,32)(25,26)(30,31)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26380);