Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1389 |
128 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,7,18,8,17,22,33,10,20,24,16,9,19,23,26)(5,11,12,28,25,31,35,32,14,29,30,15,13,27,21,34);(2,3)(4,5,8,13,10,14,9,25)(6,15,17,32,20,28,19,34)(7,21,22,30,24,35,23,12)(11,26,27,18,29,33,31,16)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^2,c^b=cg72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1389, C2×#67822, #10710452, … |
| maximal normal subgroup of | D3×#1389, C2×#67822, #10710452, … |
| maximal quotient of | #10682068, #10682114, #10682120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 398);