Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#405 ⋊ C2 |
| Sylow | C3 ⋊ #1765 |
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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)(8,10,12,20,13,18,11,19)(9,15,16,22,17,23,14,21);(2,3)(4,5,6,7)(9,14,17,16)(10,18)(15,22,23,21)(19,20);(2,3)(8,9,12,16,13,17,11,14)(10,15,20,22,18,23,19,21)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^2,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10710313, #10710316, #10712962, … |
| maximal normal subgroup of | #10710313, #10710316, #10712962, … |
| maximal quotient of | #10685867, #10685873, #10685884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2464);