Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C82 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C7×#1273 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C42×C7 | C22 |
| commutator | C2 | C2×C7×C82 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| socle, prime radical | C24×C7 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C42×C7 ◁ G | |
982 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(3,4)(5,6)(7,8,9,11,10,12,13,14);(4,6)(15,16,17,19,18,20,21,22)1120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 835);