Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#5133 |
| Fitting | C22×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#417 |
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(7,9)(10,13,17,16,14,15,12,11);(1,2)(10,12,14,17)(11,13,16,15);(4,5)(6,7)(8,9)(10,11)(12,13)(14,16)(15,17);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700660, #10700662, #10700701, … |
| maximal normal subgroup of | #10700660, #10700662, #10700701, … |
| maximal quotient of | C2×#70755, C2×#69854, #10761649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16343);