Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4897 |
| Fitting | C2×C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ C2×#472 |
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,9,18,14,11,13,10,7)(8,12,19,17,16,21,15,20);(6,8,10,15,11,16,18,19)(7,12,9,17,14,21,13,20);(1,2)(4,5)(6,7)(8,12)(9,10)(11,14)(13,18)(15,17)(16,21)(19,20);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10712151, #10712153, #10712214, … |
| maximal normal subgroup of | #10712151, #10712153, #10712214, … |
| maximal quotient of | C2×#68576, C2×#68579, C2×#68538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11830);