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×#61051 |
| 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 | |
2734 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)(18,25)(21,30)(23,36)(24,33)(26,32)(27,40)(28,34)(31,38)(35,41)(37,43)(39,42);(12,14)(13,18)(15,23)(16,24)(17,26)(19,31)(20,33)(21,32)(22,29)(25,30)(27,37)(28,39)(34,43)(35,42)(36,40)(38,41);(9,11)(12,15,17,28)(13,19,20,34)(14,23,26,39)(16,27,30,41)(18,31,33,43)(21,35,29,40)(22,36,32,42)(24,37,25,38);(14,24)(16,30)(18,32)(21,29)(22,33)(23,37)(25,26)(27,41)(31,42)(35,40)(36,43)(38,39);(13,20)(18,33)(19,34)(21,29)(22,32)(31,43)(35,40)(36,42)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54039);