Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2112 |
260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(9,13)(14,19)(15,20)(21,23);(5,7);(2,3)(4,5)(6,7)(8,9,10,14,11,15,16,21,12,13,17,19,18,20,22,23)Polycyclic presentation:
2^7,3|a^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682139, #10682140, #10682141, … |
| maximal normal subgroup of | #10682139, #10682140, #10682141, … |
| maximal quotient of | #10704249, #10704321, #10704389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4539);