Finite Group DatabasebetaFinite Group Databasebeta| order | 23142 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊#11716327 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C19×C29 | C2×C3 |
| LCS | G ▷ C7×C19×C29 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 3857 |
A minimal faithful permutation representation — 2 generators on 55 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(31,35,36,32,33,37)(34,43,40,38,39,45)(41,46,48,47,44,42)(50,53,54,51,52,55);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(30,31,34,40,46,43,47,33,37,42,48,36,35,41,39,44,45,38,32)(49,50,52,55,54,53,51)Polycyclic presentation:
2,3,7,19,29|c^a=c^6,d^a=d^18,e^a=e^28,c^b=c^2,d^b=d^7686 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23142, 56);