Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#452 ⋊ C2 |
| Sylow | C3 ⋊ #3009 |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(10,17)(14,21)(18,23)(20,22);(5,7)(8,10)(9,14)(11,18)(12,17)(13,20)(15,22)(16,21)(19,23);(2,3)(9,13)(11,19)(14,20)(15,16)(18,23)(21,22);(4,5)(6,7)(8,9,12,16)(10,14,17,21)(11,13,19,15)(18,20,23,22)Polycyclic presentation:
2^7,3|a^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,h^b=h^2,d^c=dg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3009, C2×#80229, #11661650, … |
| maximal normal subgroup of | D3×#3009, C2×#80229, #11661650, … |
| maximal quotient of | #10768355, #10768357, #10768443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12805);