Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#532 ◁ G | |
2060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(16,17)(18,23)(19,25)(20,27)(21,26)(22,28)(24,32)(29,37)(30,42)(31,39)(33,41)(34,38)(35,40)(36,44)(43,47)(45,46);(8,10)(9,12)(11,15)(13,14)(16,18,22,31)(17,23,28,39)(19,29,33,45)(20,34,21,30)(24,36,40,47)(25,37,41,46)(26,42,27,38)(32,44,35,43);(16,19)(17,24)(18,29)(20,32)(21,35)(22,33)(23,36)(25,26)(27,41)(28,40)(30,43)(31,45)(34,44)(37,42)(38,46)(39,47);(10,15)(12,14)(16,19)(17,25)(18,29)(20,35)(21,32)(22,33)(23,37)(24,26)(27,40)(28,41)(30,44)(31,45)(34,43)(36,42)(38,47)(39,46);(16,20,22,21)(17,26,28,27)(18,30,31,34)(19,32,33,35)(23,38,39,42)(24,25,40,41)(29,43,45,44)(36,46,47,37)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54204);