Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#4664 |
| Fitting | C2×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ C2×#381 |
1144 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 309 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:
(3,4,5)(7,9)(10,12,13,11)(15,19)(18,21);(6,7)(8,9)(10,11)(12,13)(14,16,17,20)(15,18,19,21);(1,2)(4,5)(14,15)(16,18)(17,19)(20,21);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10684797, #10685185, #10685221, … |
| maximal normal subgroup of | #10684797, #10685185, #10685221, … |
| maximal quotient of | C2×(C2×D3)⋊#95, C2×#69401, C2×#69403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5940);