Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C2×C7×#3544 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
7086 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 6 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(4,7)(5,9)(12,16)(14,22)(17,19)(20,26);(4,7)(8,10)(11,12,15,16)(13,19,21,17)(14,18,22,23)(20,25,26,24);(3,4,6,7)(5,8,9,10);(3,5)(4,8)(6,9)(7,10)(11,13,15,21)(12,17,16,19)(14,20,22,26)(18,24,23,25);(11,14)(12,18)(13,20)(15,22)(16,23)(17,24)(19,25)(21,26)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55737);