Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10466 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,12)(11,14)(13,15)(16,17)(18,27)(19,32)(20,37)(21,25)(22,26)(23,29)(24,35)(28,43)(30,39)(31,42)(33,38)(34,41)(36,46)(40,45)(44,47);(16,18,22,31)(17,23,26,39)(19,33,35,44)(20,30,21,29)(24,40,32,43)(25,42,37,27)(28,34,45,36)(38,46,47,41);(9,12)(10,15)(13,14)(16,19,20,34,22,35,21,36)(17,24,25,41,26,32,37,46)(18,28,29,44,31,45,30,33)(23,38,27,40,39,47,42,43)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3454);