Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1771 |
272 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 272 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) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(12,14,15,17,16,18,19,13);(2,3)(4,5,6,7)(9,11);(2,3)(8,9,10,11)(12,13,15,14,16,17,19,18)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=de,e^2=g,b^a=bd,c^a=cg,h^a=h^2,h^b=h^2,h^c=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1771, C2×#70467, #10793133, … |
| maximal normal subgroup of | D3×#1771, C2×#70467, #10793133, … |
| maximal quotient of | #10686323, #10686329, #10686334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3043);