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 ⋊ #3007 |
754 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)(8,11,13,12)(9,15,17,16)(10,19,20,21)(14,18,22,23);(2,3)(5,7);(8,10)(9,14)(11,19)(12,21)(13,20)(15,18)(16,23)(17,22);(4,5)(6,7)(8,9,13,17)(10,18,20,23)(11,16,12,15)(14,21,22,19)Polycyclic presentation:
2^7,3|a^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^2,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3007, C2×#80228, #11661575, … |
| maximal normal subgroup of | D3×#3007, C2×#80228, #11661575, … |
| maximal quotient of | #10767587, #10767626, #10767665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12804);