Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×2−1+4 ⋊ C2 |
| Sylow | C3 ⋊ #3010 |
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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 — 4 generators on 23 points:
(1,2,3)(10,16)(14,21)(17,22)(20,23);(5,7)(8,10)(9,14)(11,17)(12,16)(13,20)(15,21)(18,22)(19,23);(8,9,12,15)(10,14,16,21)(11,19,18,13)(17,23,22,20);(2,3)(4,5)(6,7)(9,13)(11,18)(14,20)(15,19)(17,22)(21,23)Polycyclic presentation:
2^7,3|b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,e^b=eg,d^c=dg66 conjugacy classes — view the full character table.
| maximal subgroup of | #10712758, #10712760, #10712793, … |
| maximal normal subgroup of | #10712758, #10712760, #10712793, … |
| maximal quotient of | #10768371, #10768459, #10768545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16689);