Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#556 ⋊ C2 |
| Sylow | C3 ⋊ #3324 |
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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)(6,11)(8,10)(13,19)(17,18);(2,3)(13,18)(14,15)(17,19);(4,6)(5,8)(7,11)(9,10)(12,14,16,15)(13,17,19,18);(4,5,7,9)(6,10,11,8)(12,13)(14,17)(15,18)(16,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10784805, #10784807, #10784865, … |
| maximal normal subgroup of | #10784805, #10784807, #10784865, … |
| maximal quotient of | #10810796, #10811658, #10812447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16242);