Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#3068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C2×#121 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3×C4 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,6)(3,9)(4,12)(8,14)(10,11)(13,16)(17,18,19);(1,2,4,6,5,8,12,14)(3,7,10,13,11,15,9,16);(1,3)(2,7)(4,10)(5,11)(6,13)(8,15)(9,12)(14,16);(2,8)(6,14)(7,15)(13,16)87 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17508);