Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#22551381 |
| Fitting, socle | C3×C372 ⋊ D3 |
| derived, Hall | C3×#16861552 ⋊ C2 |
| Sylow | C372 ⋊ C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#16861552 | C2 |
| Fitting, socle | C3×C372 | D3 |
| LCS | G ▷ C3×#16861552 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 222 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,7,18,28,51,61,68,72,73,62,65,46,49,16,25,38,39,21,23,9,11,2,3,14,31,44,63,71,64,74,52,69,36,57,22,29,40,54,55,34,37,17,20,4,6,27,47,59,48,70,32,58,19,41,10,15,35,45,56,66,67,50,53,30,33,8,13,42,24,60,12,43,5,26)(76,77);(75,76,77);(3,5,10)(4,7,9)(6,12,22)(8,15,21)(11,19,18)(13,24,25)(14,26,17)(16,29,38)(20,32,35)(23,36,31)(27,41,34)(28,43,30)(33,48,40)(37,52,51)(39,49,47)(42,57,54)(44,58,50)(45,60,46)(53,64,56)(55,65,63)(59,69,66)(61,70,62)(67,73,68)(71,74,72)Polycyclic presentation:
2,3^2,37^2|b^a=b^2,c^a=c^2,d^a=e,e^a=d,d^b=d^10,e^b=e^26744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 76);