Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ #3184 |
446 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 446 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) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(13,17)(16,19);(12,13,18,19,15,17,14,16);(5,8)(9,11)(13,17)(16,19);(2,3)(4,5)(6,9)(7,8)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^c=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10692675, #10692677, #10706033, … |
| maximal normal subgroup of | #10692675, #10692677, #10706033, … |
| maximal quotient of | #10795785, #10799504, #10800438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11111);