Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1885 |
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 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)(9,15)(11,12)(14,22)(19,21);(4,6,7,5)(8,10)(9,14)(11,21)(12,19)(13,20)(15,22)(16,23)(17,18);(2,3)(4,5,7,6)(8,9,12,17,13,15,11,16)(10,18,21,14,20,23,19,22)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg66 conjugacy classes — view the full character table.
| maximal subgroup of | #10710996, #10711001, #10711010, … |
| maximal normal subgroup of | #10710996, #10711001, #10711010, … |
| maximal quotient of | #10689832, #10689852, #10690102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4225);