Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4464 |
| Fitting | C2×C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ C2×#329 |
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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) = 192 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(7,10,11,12)(14,15,16,19,17,18,20,21);(4,5)(6,7)(8,10)(9,11)(12,13)(15,18)(16,20);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10686100, C4×#4464, #10686108, … |
| maximal normal subgroup of | #10686100, C4×#4464, #10686108, … |
| maximal quotient of | C2×#67479, C2×#67480, #10683154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2372);