Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4875 |
| Sylow | C3 ⋊ C2×#477 |
416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 157 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:
(1,2)(3,4,5)(6,9,10,8)(7,11,12,13)(14,15)(16,20)(17,19);(1,2)(6,8,10,9)(7,11,12,13)(14,16)(15,18)(17,20)(19,21);(4,5)(6,7,10,12)(8,11,9,13)(14,15,17,19)(16,18,20,21);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4875, #10802781, #10802854, … |
| maximal normal subgroup of | C4×#4875, #10802781, #10802854, … |
| maximal quotient of | C2×#68904, C2×#70642, C2×#68906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11739);