Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ #1504 |
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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)(6,11)(8,10);(2,3)(4,6)(5,8)(7,11)(9,10)(12,13)(14,18)(15,17)(16,19);(4,5)(6,10,11,8)(7,9)(13,16,17,18)Polycyclic presentation:
2^7,3|a^2=e,d^2=g,b^a=bd,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10686696, #10686697, #10686701, … |
| maximal normal subgroup of | #10686696, #10686697, #10686701, … |
| maximal quotient of | #10683197, #10683202, #10683237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1974);