Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#12814 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×D8 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(9,11)(12,13,14,15)(16,17)(18,26)(19,22)(20,32)(21,35)(23,28)(24,34)(25,31)(27,42)(29,46)(30,43)(33,41)(36,40)(37,44)(38,45)(39,47);(8,9,10,11)(17,22)(23,37)(24,38)(25,35)(26,42)(32,43)(39,41)(40,46);(16,18,19,27)(17,23,22,37)(20,33,30,47)(21,36,31,29)(24,40,38,46)(25,41,35,39)(26,43,42,32)(28,45,44,34)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 5802);