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×#3552 |
| 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);(3,4)(5,6)(7,8)(9,10)(12,17)(13,14)(15,23)(25,26);(4,8)(5,9)(11,12,16,17)(13,19,14,18)(15,20,23,24)(21,26,22,25);(11,13,16,14)(12,18,17,19)(15,21,23,22)(20,25,24,26);(3,5,7,9)(4,6,8,10)(11,14,16,13)(12,19,17,18)(15,22,23,21)(20,26,24,25);(3,6)(4,9)(5,8)(7,10)(11,15)(12,20)(13,21)(14,22)(16,23)(17,24)(18,25)(19,26)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55733);