Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#4483 |
| Fitting | C2×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×D4⋊C8 |
344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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)(8,13)(11,12)(14,15,16,18,17,19,20,21);(4,5)(6,7)(8,10)(9,12)(11,13);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10685778, C4×#4483, #10685788, … |
| maximal normal subgroup of | #10685778, C4×#4483, #10685788, … |
| maximal quotient of | C2×#67479, C2×#67478, #10683127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3000);