Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1804 |
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(13,17)(15,19)(16,18);(8,9,10,11)(13,16)(17,18);(2,3)(4,5,6,7)(9,11)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,e^c=eg78 conjugacy classes — view the full character table.
| maximal subgroup of | #10687151, #10687153, #10687165, … |
| maximal normal subgroup of | #10687151, #10687153, #10687165, … |
| maximal quotient of | #10687880, #10687900, #10687920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4181);