Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1967 |
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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:
(2,3)(4,5,6,7)(9,14)(13,21)(15,20)(22,23);(1,2,3)(8,10,12,19,11,16,18,17)(9,13,20,22,14,21,15,23);(5,7)(8,9,12,15,11,14,18,20)(10,13,17,22,16,21,19,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=eg,f^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1967, C2×#70065, #10798964, … |
| maximal normal subgroup of | D3×#1967, C2×#70065, #10798964, … |
| maximal quotient of | #10694017, #10694022, #10694197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2641);