Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2102 |
158 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 57 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,7,8,11,9,17,13,5)(6,12,14,19,15,16,18,10);(4,6,13,14,9,15,8,18)(5,10,17,12,11,19,7,16);(2,3)(4,5,8,7,9,11,13,17)(6,12,14,19,15,16,18,10)Polycyclic presentation:
2^7,3|a^2=d,b^2=de,c^2=d,d^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,f^c=fg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2102, C2×#69024, #10825156, … |
| maximal normal subgroup of | D3×#2102, C2×#69024, #10825156, … |
| maximal quotient of | #10700314, #10700319, #10700324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1600);