Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C43 |
| direct product | C2×C7×#2867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
8094 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 21 points:
(1,2)(15,16,17,18,19,20,21);(4,6)(8,9)(12,13);(7,8,10,9);(11,12,14,13);(3,4,5,6)(7,9,10,8)(11,13,14,12)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29630);