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×#3562 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
7354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(4,7)(5,9)(11,12)(13,16)(14,19)(15,20)(17,21)(18,23)(22,24)(25,26);(4,7)(8,10)(12,13)(14,21)(18,20)(22,26);(3,4)(5,8)(6,7)(9,10)(11,13,16,12)(14,19,21,17)(15,20,23,18)(22,25,26,24);(3,5,6,9)(4,8,7,10)(11,14)(12,17)(13,19)(15,22)(16,21)(18,24)(20,25)(23,26);(11,15,16,23)(12,18,13,20)(14,22,21,26)(17,24,19,25)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55728);