Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4745 |
| Fitting | C2×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ C2×#413 |
756 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 213 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)(6,8,9,15,10,16,18,21)(7,12,13,19,11,14,17,20);(6,7)(8,14)(9,17)(10,11)(12,16)(13,18)(15,19)(20,21);(1,2)(4,5)(7,11)(12,14)(13,17)(19,20);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10710128, #10710136, #10712668, … |
| maximal normal subgroup of | #10710128, #10710136, #10712668, … |
| maximal quotient of | C2×#68100, C2×#68119, #10760997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11272);