Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C3 ⋊ #1744 |
296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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 — 3 generators on 23 points:
(2,3)(16,18,19,22)(17,21,20,23);(1,2,3)(4,5,6,7)(17,20)(21,23);(8,9,10,12,11,13,14,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^c=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10683123, #10683125, #10683131, … |
| maximal normal subgroup of | #10683123, #10683125, #10683131, … |
| maximal quotient of | #10685609, #10685611, #10685615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1172);