Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C59×#17593 |
| 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×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C42×C59 ◁ G | |
1042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,8,10,22)(3,13)(4,18)(5,19)(9,24,25,32)(11,23,12,20)(15,29)(16,30)(17,28)(21,26,31,27)(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)(4,8)(5,20)(6,11)(7,12)(10,14)(13,27)(15,21)(16,24)(17,26)(18,23)(19,22)(25,28)(29,31)(30,32);(1,3,14,28)(2,9,10,25)(4,15,19,29)(5,16,18,30)(6,17,7,13)(8,21,22,31)(11,26,12,27)(20,24,23,32);(1,4,7,5)(2,8,12,20)(3,15,13,16)(6,18,14,19)(9,21,27,24)(10,22,11,23)(17,30,28,29)(25,31,26,32)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10581);