Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4478 |
| Sylow | C3 ⋊ C2×#356 |
240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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) = 96 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(6,8,9,15,11,17,7,12)(10,16,13,14,19,20,18,21);(4,5)(6,7,11,9)(8,14,17,21)(10,18,19,13)(12,20,15,16);(1,2)48 conjugacy classes — view the full character table.
| maximal subgroup of | #10710368, C4×#4478, #10710372, … |
| maximal normal subgroup of | #10710368, C4×#4478, #10710372, … |
| maximal quotient of | C2×#67455, C2×#67453, #10704467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2705);