Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#467 ⋊ C2 |
| Sylow | C3 ⋊ #3056 |
496 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)(13,22)(16,23)(18,21);(5,7);(8,10,11,18,12,17,20,21)(9,13,14,16,15,22,19,23);(2,3)(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,h^a=h^2,d^b=dg,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3056, C2×#80759, #11662350, … |
| maximal normal subgroup of | D3×#3056, C2×#80759, #11662350, … |
| maximal quotient of | #10777963, #10777985, #10778007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13335);