Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#4529 |
| Sylow | C3 ⋊ C2×#340 |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(6,7)(8,9)(10,11,12,13)(15,18)(16,21)(19,20);(4,5)(7,9)(14,15,16,19,17,20,21,18);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#340, C4×#4529, #10700369, … |
| maximal normal subgroup of | Dic3×#340, C4×#4529, #10700369, … |
| maximal quotient of | C2×#67703, #10684652, #10684662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4133);