Finite Group DatabasebetaFinite Group Databasebeta| order | 24990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C17⋊#64424) |
| unambiguous semidirect product | C17⋊(C5⋊#64424) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C17 | C2×C3 |
| LCS | G ▷ C5×C72×C17 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 4165 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20)(21,22)(24,27,28,25,26,29)(31,34,35,32,33,36);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,21,22,20)(30,31,33,36,35,34,32);(23,24,26,29,28,27,25)Polycyclic presentation:
2,3,5,7^2,17|c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^16,d^b=d^2,e^b=e^2812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24990, 58);