Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3182 |
402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 402 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:
(1,2,3)(4,6,7,10)(5,9,8,11)(13,17)(16,19);(2,3)(12,13,14,16,15,17,18,19);(5,8)(9,11)(13,17)(16,19);(4,5)(6,9)(7,8)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^c=dg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10692660, #10692662, #10692680, … |
| maximal normal subgroup of | #10692660, #10692662, #10692680, … |
| maximal quotient of | #10795781, #10799520, #10800429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15870);