Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1277 |
180 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 113 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) = 384 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(4,5,6,7)(16,17,19,22,20,23,18,21);(2,3)(8,9,10,12,11,13,14,15)(17,21)(18,19)(22,23)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=ef,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10681954, #10681955, #10681957, … |
| maximal normal subgroup of | #10681954, #10681955, #10681957, … |
| maximal quotient of | #10681715, #10681721, #10681725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 230);