Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1828 |
296 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 81 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:
(2,3)(4,7)(5,10,11,15)(6,13)(8,16)(9,17,12,18)(14,19);(1,2,3)(4,6)(5,9)(7,13)(8,14)(10,17)(11,12)(15,18)(16,19);(4,5)(6,12,14,9)(7,15)(8,11)(10,16)(13,17,19,18)Polycyclic presentation:
2^7,3|a^2=f,c^2=d,b^a=bd,c^a=ce,d^a=dg,f^b=fg,e^c=eg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | #10710801, #10710803, #10710806, … |
| maximal normal subgroup of | #10710801, #10710803, #10710806, … |
| maximal quotient of | #10688644, #10688647, #10688650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2596);