Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16810003⋊C7 |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C4×C7 |
| Hall | C5×C132⋊C7 ⋊ C4 |
| Hall | #16810003 ⋊ C7 |
| Hall | C132⋊C7 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C7×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #10621728⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C4×C7 |
| prime radical | C5⋊((C13⋊D13)⋊C7) | C2 |
| cosocle | C5⋊(C13⋊D13) | C2×C7 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 455 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,2,4,11,28,48,62)(3,20,47,59,49,79,90,21,8,33,61,71,66,89,9,41,23,57,67,82,80,7,24,35,46,65,81,91)(5,12,52,58,69,78,42,36,15,32,70,74,84,44,16,13,29,56,77,86,43,14,31,34,51,64,88,22)(6,39,53,50,75,85,26,25,18,30,72,68,87,10,19,37,40,54,63,83,45,17,38,55,60,73,76,27)(93,94,95,96);(1,3,10,26,44,21,42,43,7,22,45,27,9)(2,5,8,20,17,36,19,6,14,25,41,24,16)(4,12,33,47,38,15,37,39,31,18,23,35,13)(11,29,46,57,30,34,53,40,32,55,59,61,52)(28,49,54,72,56,71,70,51,65,58,60,50,67)(48,63,77,74,81,73,82,79,68,66,64,69,75)(62,76,88,86,90,85,91,89,83,80,78,84,87)(92,93,94,96,95)Polycyclic presentation:
2,7,2,5,13^2|a^2=c,d^a=d^2,e^a=e^8,f^a=f^8,e^b=e^3f^11,f^b=e^3f^7,d^c=d^4,e^c=e^12,f^c=f^1265 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 63);