Finite Group DatabasebetaFinite Group Databasebeta| order | 21462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C73⋊C3)⋊D49 |
| Fitting, derived, Hall | C49×C73 ⋊ C2×C3 |
| Hall | C49×C73⋊C3 ⋊ C2 |
| Hall | D3577 ⋊ C3 |
| Hall | C73⋊C3 ⋊ D49 |
| Sylow | C73 ⋊ C3×D49 |
| Sylow | C49 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C73 | C2×C3 |
| Frattini | C7 | (C73⋊C3)⋊D7 |
| socle | C7×C73 | C3×D7 |
| LCS | G ▷ C49×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 122 |
| transitive degree | μt(G) = 3577 |
A minimal faithful permutation representation — 2 generators on 122 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,60)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,48,57,34,49,63)(37,42,62,50,51,58)(40,67,65,54,55,53)(52,61,68,56,64,72)(59,73,71,69,70,66)(75,77)(76,80)(78,83)(79,86)(81,89)(82,88)(84,93)(85,96)(87,98)(90,102)(91,101)(92,100)(94,95)(97,107)(99,109)(103,110)(104,112)(105,111)(106,115)(108,117)(113,118)(114,119)(116,121)(120,122);(1,2,5,11,19,32,33,20,4,8,13,23,37,52,54,36,10,16,24,38,53,66,69,51,18,29,39,41,57,68,73,64,31,48,55,58,60,47,62,67,49,46,61,70,72,63,28,43,44,27,42,59,71,65,45,15,26,14,25,40,56,50,35,22,7,6,12,21,34,30,17,9,3)(74,88,112,122,114,92,77,80,101,118,116,105,83,86,89,110,108,106,93,96,98,102,99,97,95,94,107,109,90,87,85,84,115,117,103,81,79,78,111,121,113,91,76,75,100,119,120,104,82)Polycyclic presentation:
2,3,7,73,7|c^7=e^6,c^a=c^6e,d^a=d^72,e^a=e^6,d^b=d^8666 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21462, 21);