Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1451 |
208 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,8)(9,11);(12,13,14,17,15,16,18,19);(2,3)(4,5,6,9,7,8,10,11)(13,16)(17,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682080, #10682081, #10682086, … |
| maximal normal subgroup of | #10682080, #10682081, #10682086, … |
| maximal quotient of | #10684549, #10684569, #10685613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2301);