Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C11 |
| unambiguous semidirect product | C5⋊(C5⋊((C11⋊D11)⋊C3)) |
| Fitting, socle, derived, Hall | C52×C112 ⋊ C2×C3 |
| Hall | C52×C112⋊C3 ⋊ C2 |
| Hall | C5⋊(C5⋊(C11⋊D11)) ⋊ C3 |
| Hall | C112⋊C3 ⋊ C5⋊D5 |
| Sylow | C112 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ (C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C112 | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 825 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,4)(3,15,17,7,8,24)(5,23,20,12,13,30)(6,11,21,16,10,22)(9,27,29,18,19,33)(14,28,32,25,26,31)(35,36)(37,38)(40,41)(42,43);(1,3,9,20,22,31,32,21,30,18,7)(2,5,14,27,8,16,6,15,19,25,12)(4,10,13,24,26,29,33,28,17,23,11)(39,40,42,43,41);(34,35,37,38,36)Polycyclic presentation:
2,3,5^2,11^2|c^a=c^4,d^a=d^4,e^a=e^10,f^a=f^10,e^b=e^7f^5,f^b=e^4f^3542 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 167);