Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#448 ⋊ C2 |
| Sylow | C3 ⋊ #3103 |
428 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 129 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) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,3)(4,6,7,10)(5,9,8,11);(1,2,3)(12,13,15,17)(14,19,18,16);(5,8)(9,11);(4,5)(6,9)(7,8)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^d=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | #10767461, #10767463, #10767499, … |
| maximal normal subgroup of | #10767461, #10767463, #10767499, … |
| maximal quotient of | #10795194, #10798130, #10798134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12604);