Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4774 |
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ C2×#480 |
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,8)(7,11)(9,13)(10,12)(14,15)(16,21)(17,19)(18,20);(1,2)(6,8,9,13)(7,10,12,11)(15,18)(16,20)(19,21);(4,5)(6,7)(8,10)(9,12)(11,13);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4774, #10802299, #10802366, … |
| maximal normal subgroup of | C4×#4774, #10802299, #10802366, … |
| maximal quotient of | C2×#68871, C2×#68874, C2×#70200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11329);