Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#1770 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4 | C23 |
| commutator | C22 | C2×C3×C42 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| socle, prime radical | C23×C3 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4 ◁ G | |
272 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(5,6,7,8)(9,10,13,15,12,14,16,11)(17,18,19);(1,2,3,4)(6,8)(10,14)(11,15);(9,11,16,14,12,15,13,10)168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5061);