Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ #3114 |
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(12,14,16,15)(13,18,19,17);(13,17)(14,15)(18,19);(5,8)(9,11);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^c=dg,f^c=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10693294, #10693300, #10767769, … |
| maximal normal subgroup of | #10693294, #10693300, #10767769, … |
| maximal quotient of | #10795238, #10798203, #10798218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14887);