Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4857 |
| Sylow | C3 ⋊ C2×#479 |
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(3,4,5)(6,9,10,8)(7,11,12,13)(14,16,18,23)(15,19,21,27)(17,25,24,22)(20,29,28,26);(1,2)(6,8,10,9)(7,11,12,13)(16,22)(17,24)(19,26)(20,28)(23,25)(27,29);(4,5)(6,7,10,12)(8,11,9,13)(14,15,18,21)(16,19,23,27)(17,20,24,28)(22,26,25,29);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10802807, C4×#4857, #10802881, … |
| maximal normal subgroup of | #10802807, C4×#4857, #10802881, … |
| maximal quotient of | C2×#68905, C2×#68906, C2×#70588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11708);