Finite Group DatabasebetaFinite Group Databasebeta| order | 13005 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3×C17 |
| Fitting, socle | C3×C5×C172 ⋊ C3 |
| derived, Sylow | C172 ⋊ C32×C5 |
| Hall | C5×C172 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C172⋊C3 |
| commutator, cosocle, hypocenter | C172 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 765 |
A minimal faithful permutation representation — 2 generators on 59 points:
(1,2,4)(3,7,15)(5,11,22)(6,9,8)(10,20,16)(12,25,38)(13,23,34)(14,19,32)(17,29,18)(21,35,27)(24,36,30)(26,40,50)(28,33,46)(31,42,45)(37,47,41)(39,48,43)(44,49,51)(52,53,54,55,56);(1,3,8,18,32,45,46,51,50,48,47,38,36,35,22,20,34)(2,14,26,30,13,17,44,12,16,6,28,41,5,7,31,43,27)(4,24,49,9,11,39,19,23,25,33,15,21,40,29,10,37,42)(57,58,59)1485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13005, 7);