Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#137 ⋊ C2 |
| Sylow | C3 ⋊ #3056 |
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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)(10,17)(13,22)(16,23)(18,21);(2,3)(5,7);(8,10,11,18,12,17,20,21)(9,13,14,16,15,22,19,23);(4,5)(6,7)(8,9,12,15)(10,16,17,23)(11,19,20,14)(13,21,22,18)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10832620, #10832623, #10832642, … |
| maximal normal subgroup of | #10832620, #10832623, #10832642, … |
| maximal quotient of | #10777960, #10777982, #10778004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16561);