Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1503 |
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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 — 3 generators on 19 points:
(2,3)(12,14,16,15)(13,17,18,19);(1,2,3)(4,5,7,9)(6,11,10,8)(12,13)(14,17)(15,19)(16,18);(5,8)(6,10)(9,11)(13,17,18,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=fg,d^2=g,b^a=bd,d^a=df,d^b=dg,e^b=efg,h^c=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1503, C2×#68309, #10762293, … |
| maximal normal subgroup of | D3×#1503, C2×#68309, #10762293, … |
| maximal quotient of | #10683131, #10683133, #10683163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 885);