Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#11003 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #392 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C2×C59 | #1438 |
| prime radical | C59×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G | |
1292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2)(3,12)(4,16,19,27)(5,20)(6,10)(7,11)(8,14)(9,18,26,17)(13,25,30,22)(15,23)(21,24)(28,29,32,31)(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)(5,21)(6,14)(7,15)(9,25)(10,23)(11,24)(12,20)(16,32)(17,31)(18,29)(19,30)(22,26)(27,28);(1,4)(2,9)(3,13)(5,18)(6,17)(7,19)(8,22)(10,27)(11,26)(12,28)(14,31)(15,30)(16,20)(21,29)(23,32)(24,25)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 3991);