Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4752 |
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ C2×#456 |
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,9,10,19,11,20,21,12)(7,13,14,18,15,8,16,17);(1,2)(6,8,11,13)(7,12,15,19)(9,14,20,16)(10,18,21,17);(4,5)(6,7)(8,12)(9,18)(10,16)(11,15)(13,19)(14,21)(17,20);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10712533, #10712543, #10714224, … |
| maximal normal subgroup of | #10712533, #10712543, #10714224, … |
| maximal quotient of | C2×#68132, C2×#68134, C2×#68133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11284);