Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C2×C7×#2977 |
| 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×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
2362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 448 |
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)(11,12,14,17,15,18,21,24)(13,16,20,23,19,22,25,26);(3,5)(4,7)(6,10)(8,9)(11,13)(12,16)(14,20)(15,19)(17,23)(18,22)(21,25)(24,26);(5,10)(7,9)(13,19)(16,22)(20,25)(23,26);(4,8)(7,9)(13,19)(16,22)(20,25)(23,26)700 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53213);