Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#61053 |
| 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×#525 ◁ G | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13)(14,22)(15,19)(16,29)(17,20)(18,24)(21,32)(23,40)(25,38)(26,43)(27,39)(28,36)(30,34)(31,37)(33,42)(35,41);(12,14,17,25)(13,18,20,34)(15,26,28,42)(16,30,32,24)(19,35,36,40)(21,38,29,22)(23,31,41,27)(33,39,43,37);(9,11);(12,15,17,28)(13,19,20,36)(14,23,25,41)(16,31,32,27)(18,33,34,43)(21,39,29,37)(22,40,38,35)(24,42,30,26);(13,20)(18,34)(19,36)(21,29)(22,38)(33,43)(35,40)(37,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54041);