Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4799 |
| Sylow | C3 ⋊ C2×#479 |
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 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) = 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)(16,22)(18,25)(19,26)(21,29)(23,24)(27,28);(1,2)(6,8)(7,11)(9,10)(12,13)(14,16,17,23)(15,19,20,27)(18,22,25,24)(21,26,29,28);(4,5)(6,7,10,12)(8,11,9,13)(14,15,17,20)(16,19,23,27)(18,21,25,29)(22,26,24,28);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4799, #10802813, #10802878, … |
| maximal normal subgroup of | C4×#4799, #10802813, #10802878, … |
| maximal quotient of | C2×#70222, C2×#70235, C2×#70238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11353);