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×#3547 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
7182 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)(11,12,15,16)(13,19,20,17)(14,22,23,18)(21,24,26,25);(4,7)(8,10)(12,16)(13,20)(18,22)(21,26);(3,4,6,7)(5,8,9,10)(11,13,15,20)(12,17,16,19)(14,21,23,26)(18,24,22,25);(3,5)(4,8)(6,9)(7,10)(11,12)(13,17)(14,18)(15,16)(19,20)(21,24)(22,23)(25,26);(11,14,15,23)(12,18,16,22)(13,21,20,26)(17,24,19,25)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55738);