Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#461 ⋊ C2 |
| Sylow | C3 ⋊ #3042 |
494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(2,3)(10,17)(13,21)(18,23)(20,22);(1,2,3)(9,14)(11,19)(13,20)(15,16)(18,23)(21,22);(4,5,6,7)(8,10)(9,13)(11,18)(12,17)(14,20)(15,22)(16,21)(19,23);(5,7)(8,9,12,16)(10,13,17,21)(11,14,19,15)(18,20,23,22)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3042, C2×#80430, #11662131, … |
| maximal normal subgroup of | D3×#3042, C2×#80430, #11662131, … |
| maximal quotient of | #10780400, #10780409, #10780418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13006);