Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C2×C7×#1363 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(4,7)(5,9)(8,10)(11,12,15,19,18,23,25,26,16,20,14,24,17,13,21,22);(3,4,6,8)(5,10,9,7)(11,13,16,23)(12,18,20,17)(14,24,15,19)(21,26,25,22)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4921);