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×#3553 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
6566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 6 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4)(5,10)(6,11)(7,15)(8,9)(12,16)(13,14)(17,18)(20,24)(21,27)(22,30)(32,34);(4,9)(6,10)(12,15)(14,17)(19,20,23,24)(21,28,27,25)(22,26,30,31)(29,34,33,32);(3,5,8,11)(4,10,9,6)(7,13,16,18)(12,17,15,14)(19,20)(21,25)(22,26)(23,24)(27,28)(29,32)(30,31)(33,34);(3,6,8,10)(4,11,9,5)(7,14,16,17)(12,18,15,13)(19,21,23,27)(20,25,24,28)(22,29,30,33)(26,32,31,34);(3,7)(4,12)(5,13)(6,14)(8,16)(9,15)(10,17)(11,18)(19,22)(20,26)(21,29)(23,30)(24,31)(25,32)(27,33)(28,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55742);