Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ #3282 |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(9,14)(10,17)(11,21)(13,16)(18,19)(22,23);(5,7);(8,10,12,19)(9,13,14,22)(11,17,21,18)(15,23,20,16);(2,3)(4,5)(6,7)(8,9,12,14)(10,16,19,23)(11,20,21,15)(13,17,22,18)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^2,d^b=de,e^b=eg,e^d=eg63 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3282, C2×#83867, #67×#135, … |
| maximal normal subgroup of | D3×#3282, C2×#83867, #67×#135, … |
| maximal quotient of | #10785010, #10785025, #10785040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16443);