Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5160 |
| Fitting | C22×C3×D8 ⋊ 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)(7,12)(8,15)(9,18)(13,14)(16,17)(19,20);(1,2)(6,8,9,16,10,17,18,15)(7,11,12,20,14,21,13,19);(1,2)(4,5)(6,7)(8,11)(9,12)(10,14)(13,18)(15,19)(16,20)(17,21);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10712149, #10712155, #10712212, … |
| maximal normal subgroup of | #10712149, #10712155, #10712212, … |
| maximal quotient of | C2×#71282, C2×#71372, C2×#71200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16416);