Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C22⋊Q8 ⋊ C2 |
| Sylow | C3 ⋊ #3187 |
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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)(5,9)(8,10);(2,3)(6,11)(8,10)(13,16)(14,19)(17,18);(4,6)(5,8)(7,11)(9,10);(4,5)(6,10)(7,9)(8,11)(12,13,15,18)(14,16,19,17)Polycyclic presentation:
2^7,3|a^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10691743, #10691749, #10691765, … |
| maximal normal subgroup of | #10691743, #10691749, #10691765, … |
| maximal quotient of | #10804188, #10804199, #10805446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15312);