Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1795 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#10777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #379 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(12,13,17,23,18,21,16,22)(14,24,26,37,27,19,32,34)(15,28,30,20,31,36,29,35)(25,39,40,33,41,43,42,38);(8,9,10,11)(12,14)(13,19)(15,25)(16,26)(17,32)(18,27)(20,33)(21,24)(22,34)(23,37)(28,43)(29,40)(30,42)(31,41)(35,38)(36,39);(12,15,18,31)(13,20,21,35)(14,25,27,41)(16,30,17,29)(19,33,24,38)(22,36,23,28)(26,42,32,40)(34,39,37,43)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3765);