Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#358 |
| Fitting | C3×#358 ⋊ C2 |
| Sylow | C3 ⋊ C2×#358 |
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(5,6,9,12)(7,14,16,20)(8,17,15,11)(10,18,19,13)(21,22,23);(1,2,3,4)(6,10)(7,13)(8,15)(11,20)(12,19)(14,17)(16,18);(22,23)66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#358, D3×#2138, D3×#2141, … |
| maximal normal subgroup of | C2×D3×#358, D3×#2138, D3×#2141, … |
| maximal quotient of | D3×#1332, #10705164, #10705216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1795);