Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#135 ⋊ C2 |
| Sylow | C3 ⋊ #3061 |
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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 — 4 generators on 23 points:
(1,2,3)(8,10,12,17)(9,15,16,22)(11,18,14,21)(13,19,20,23);(2,3)(5,7)(10,17)(15,22)(18,21)(19,23);(8,9,14,20,12,16,11,13)(10,15,21,23,17,22,18,19);(4,5)(6,7)(9,13)(11,14)(15,19)(16,20)(18,21)(22,23)Polycyclic presentation:
2^7,3|b^2=eg,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10713898, #10713902, #10713905, … |
| maximal normal subgroup of | #10713898, #10713902, #10713905, … |
| maximal quotient of | #10778276, #10778315, #10778370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16493);