Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | Dic3×#108 |
| Sylow | C3 ⋊ C4×#108 |
228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(5,7,8,15,10,17,9,16)(6,11,12,14,13,19,18,20)(21,22,23);(5,6,9,12,10,13,8,18)(7,14,16,19,17,20,15,11);(1,2,3,4)(22,23)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710410, Dic3×#359, #10710415, … |
| maximal normal subgroup of | #10710410, Dic3×#359, #10710415, … |
| maximal quotient of | Dic3×#334, Dic3×#335, #10686378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3267);