Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C2×C7×#2981 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C2×C7×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
2230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(3,4)(5,9)(6,8)(7,10)(11,12,15,19,14,18,22,26)(13,17,21,25,20,16,23,24);(3,5)(4,7)(6,10)(8,9)(11,13)(12,16)(14,20)(15,21)(17,18)(19,24)(22,23)(25,26);(5,10)(7,9)(11,13)(12,17)(14,20)(15,21)(16,18)(19,25)(22,23)(24,26);(4,8)(7,9)(12,18)(13,20)(19,26)(21,23)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53217);