Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#533 ⋊ C2 |
| Sylow | C3 ⋊ #3138 |
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,19)(14,18);(2,3)(5,9)(8,11)(12,14,15,13,17,18,16,19);(2,3)(4,6,7,10)(5,8,9,11)(12,13,16,14,17,19,15,18);(2,3)(4,5)(6,8)(7,9)(10,11)(13,18)(14,19)(15,16)Polycyclic presentation:
2^7,3|b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,d^b=dg,h^b=h^2,d^c=dg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10692717, #10692719, #10692721, … |
| maximal normal subgroup of | #10692717, #10692719, #10692721, … |
| maximal quotient of | #10795403, #10797912, #10798873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15912);