Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4898 |
| Fitting | C2×C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ C2×#471 |
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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)(6,9,10,20,12,21,11,13)(7,14,15,19,16,8,17,18);(6,8,11,19,12,14,10,18)(7,13,15,9,16,20,17,21);(1,2)(4,5)(6,7)(8,13)(9,19)(10,17)(11,15)(12,16)(14,20)(18,21);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10802047, C4×#4898, #10802106, … |
| maximal normal subgroup of | #10802047, C4×#4898, #10802106, … |
| maximal quotient of | C2×#68536, C2×#68537, C2×#68580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11829);