Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10447 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,12)(11,13)(14,15)(16,17,21,25)(18,26,29,41)(19,30,33,23)(20,34,36,24)(22,35,38,28)(27,43,31,42)(32,40,47,45)(37,44,39,46);(9,12)(13,14)(16,18,21,29)(17,22,25,38)(19,31,33,27)(20,35,36,28)(23,39,30,37)(24,41,34,26)(32,44,47,46)(40,42,45,43);(9,13)(11,15)(12,14)(16,19,20,32,21,33,36,47)(17,23,24,40,25,30,34,45)(18,27,28,44,29,31,35,46)(22,37,26,42,38,39,41,43)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3435);