Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4754 |
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ C2×#471 |
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 133 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)(6,9,11,12)(7,13,15,16)(8,14,17,18)(10,20,21,19);(6,8,10,16,11,17,21,13)(7,12,14,20,15,9,18,19);(1,2)(4,5)(6,7)(8,12)(9,17)(10,14)(11,15)(13,19)(16,20)(18,21);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10802051, C4×#4754, #10802110, … |
| maximal normal subgroup of | #10802051, C4×#4754, #10802110, … |
| maximal quotient of | C2×#68440, C2×#68442, C2×#68446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11286);