Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#4551 |
| 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)(14,15,16,18,17,19,20,21);(4,5)(7,9)(10,11,12,13)(15,18)(16,20)(19,21);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682330, #10682332, #10682348, … |
| maximal normal subgroup of | #10682330, #10682332, #10682348, … |
| maximal quotient of | C2×#67654, #10684653, #10684663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4544);