Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1374 |
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(4,5,6,7)(9,11);(2,3)(8,9)(10,11)(12,13,14,17,15,18,20,23,16,19,21,24,22,25,26,27)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^a=h^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #10681930, #10681931, #10681953, … |
| maximal normal subgroup of | #10681930, #10681931, #10681953, … |
| maximal quotient of | #10682015, #10682029, #10682036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 233);