Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16810002⋊C7 |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C4×C7 |
| Hall | C5×C132⋊C7 ⋊ C4 |
| Hall | #16810002 ⋊ 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:
(1,2,4,11,31,48,62)(3,21,46,56,49,80,91,22,8,38,61,72,66,90,9,26,24,59,67,79,81,7,25,35,45,65,82,89)(5,13,52,55,70,86,23,17,15,37,71,64,84,42,16,12,32,57,77,78,44,14,36,34,51,74,88,43)(6,39,58,53,75,83,30,28,19,54,68,73,87,29,20,47,41,50,63,85,27,18,40,33,60,69,76,10)(93,94,95,96);(1,3,10,30,43,7,23,44,22,42,27,29,9)(2,5,8,26,28,14,20,6,17,18,21,25,16)(4,12,35,46,40,15,39,47,36,19,24,38,13)(11,32,45,56,33,37,58,41,34,54,59,61,52)(31,49,53,68,55,65,71,51,72,57,60,50,67)(48,63,77,74,82,73,80,79,69,66,64,70,75)(62,76,88,86,91,85,90,89,83,81,78,84,87)(92,93,94,96,95)Polycyclic presentation:
2,7,2,5,13^2|a^2=c,d^a=d^2,e^a=e^5,f^a=f^5,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, 62);