Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ #2888 |
756 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 289 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 — 4 generators on 19 points:
(1,2,3)(6,12)(10,15)(13,18)(17,19);(4,6)(5,10)(7,13)(8,12)(9,15)(11,17)(14,18)(16,19);(5,9)(7,14)(10,15)(13,18);(2,3)(4,5,7,11,8,9,14,16)(6,10,13,17,12,15,18,19)Polycyclic presentation:
2^7,3|a^2=f,f^2=g,b^a=be,e^a=eg,h^a=h^2,f^b=fg,d^c=dg75 conjugacy classes — view the full character table.
| maximal subgroup of | #10712751, #10712755, #10712765, … |
| maximal normal subgroup of | #10712751, #10712755, #10712765, … |
| maximal quotient of | #10761006, #10761020, #10761094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16676);