Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#339 ⋊ C2 |
| Sylow | C3 ⋊ #1861 |
262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(4,7)(5,12)(6,16)(8,19)(9,15)(10,11)(13,18)(14,17);(4,6,9,12,10,18,8,17)(5,11,13,19,14,7,16,15);(2,3)(4,5,9,13,10,14,8,16)(6,15,12,11,18,19,17,7)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg,e^c=eg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1861, C2×#68773, #10796088, … |
| maximal normal subgroup of | D3×#1861, C2×#68773, #10796088, … |
| maximal quotient of | #10689071, #10689078, #10689085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1349);