Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C2×C7×Q8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×Q8 ◁ G | |
1830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(3,4,5,6)(7,10,9,8);(3,7,5,9)(4,8,6,10);(11,12,13,14,15,16,17,18)(19,26,25,24,23,22,21,20);(11,19,15,23)(12,20,16,24)(13,21,17,25)(14,22,18,26)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54343);