Finite Group DatabasebetaFinite Group Databasebeta| order | 22386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊#10587722 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C41 | C2×C3 |
| LCS | G ▷ C7×C13×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 3731 |
A minimal faithful permutation representation — 2 generators on 61 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)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(43,47,48,44,45,49)(46,53,52,50,51,54)(56,59,60,57,58,61);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(42,43,46,45,49,52,51,53,54,48,47,50,44)(55,56,58,61,60,59,57)Polycyclic presentation:
2,3,7,13,41|c^a=c^6,d^a=d^12,e^a=e^40,c^b=c^2,d^b=d^3681 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22386, 47);