Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2273 |
912 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 389 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) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,17)(16,18);(14,19)(16,18);(8,9,10,11)(12,14)(13,16)(15,19)(17,18);(2,3)(4,5,6,7)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,b^a=be,d^a=de,h^a=h^2,c^b=ce108 conjugacy classes — view the full character table.
| maximal subgroup of | #10688644, #10692620, #10692623, … |
| maximal normal subgroup of | #10688644, #10692620, #10692623, … |
| maximal quotient of | #10716269, #10716270, #10716426, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14659);