Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×#4648 |
| Sylow | C3 ⋊ C2×#376 |
840 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 405 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7,8,9)(14,16)(15,18)(17,20)(19,21);(10,11,12,13)(16,20)(18,21);(1,2)(4,5)(14,15,17,19)(16,18,20,21);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684776, #10684788, #10685177, … |
| maximal normal subgroup of | #10684776, #10684788, #10685177, … |
| maximal quotient of | C2×Dic3×#95, C4×#4648, C2×#69402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5895);