Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10061 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)(28,29,33,37)(30,38,41,42)(31,34,32,36)(35,39,43,40);(8,9)(10,11)(12,14,17,23)(13,18,20,27)(15,22,16,25)(19,26,24,21)(29,34)(31,32)(35,42)(36,37)(38,43)(39,40);(9,11)(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(28,30,33,41)(29,35,37,43)(31,40,32,39)(34,42,36,38)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3049);