Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#124 ⋊ C2 |
| Sylow | C3 ⋊ #2003 |
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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)(5,7)(8,10,12,18)(9,14,16,23)(11,20,19,17)(13,21,15,22);(9,13)(11,19)(14,22)(15,16)(17,20)(21,23);(2,3)(4,5)(6,7)(8,9)(10,14)(11,13)(12,16)(15,19)(17,22)(18,23)(20,21)Polycyclic presentation:
2^7,3|c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2003, C2×#71730, #10822093, … |
| maximal normal subgroup of | D3×#2003, C2×#71730, #10822093, … |
| maximal quotient of | #10695390, #10695432, #10695446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4306);