Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4735 |
| Fitting | C2×C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#481 |
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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)(7,11)(8,13)(14,15,16,18,17,19,20,21);(1,2)(6,8)(7,10)(9,13)(11,12);(4,5)(6,7)(8,12)(9,11)(10,13)(15,18)(16,20)(19,21);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10690351, #10690353, #10691647, … |
| maximal normal subgroup of | #10690351, #10690353, #10691647, … |
| maximal quotient of | C2×#69925, C2×#69928, C2×#69932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11165);