Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1377 |
140 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 77 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) = 192 |
A minimal faithful permutation representation — 2 generators on 23 points:
(2,3)(4,5,6,7)(9,13)(10,16)(15,20)(17,22);(1,2,3)(8,9,10,14,11,15,17,21,12,13,16,19,18,20,22,23)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1377, C2×#67812, #10710047, … |
| maximal normal subgroup of | D3×#1377, C2×#67812, #10710047, … |
| maximal quotient of | #10682020, #10682030, #10682037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 388);