Finite Group DatabasebetaFinite Group Databasebeta| order | 12558 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#10587717 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C23 | C2×C3 |
| LCS | G ▷ C7×C13×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2093 |
A minimal faithful permutation representation — 2 generators on 43 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,29,30,26,27,31)(28,34,35,32,33,36)(38,39,40)(41,43,42);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,28,30,29,33,35,36,34,27,31,32,26)(37,38,39,41,40,42,43)Polycyclic presentation:
2,3,7,13,23|d^a=d^12,e^a=e^22,c^b=c^2,d^b=d^9387 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12558, 32);