Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C3×C4×C8 ⋊ C2 |
| Sylow | C3 ⋊ #1974 |
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,10,12,20,13,21,11,19)(9,15,14,18,17,23,16,22);(5,7)(9,14,17,16)(15,18,23,22);(2,3)(4,5,6,7)(8,9,12,16,13,17,11,14)(10,18,20,15,21,22,19,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=e,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10681959, #10681961, #10712236, … |
| maximal normal subgroup of | #10681959, #10681961, #10712236, … |
| maximal quotient of | #10694038, #10694045, #10694050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2371);