Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #2296 |
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 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)(12,14,15,18)(13,17,16,19);(13,16)(17,19);(4,6,7,5)(9,11);(2,3)(4,5,7,6)(8,9)(10,11)(12,13)(14,17)(15,16)(18,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,d^2=f,b^a=be,c^a=cf,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10683141, #10683202, #10683205, … |
| maximal normal subgroup of | #10683141, #10683202, #10683205, … |
| maximal quotient of | #10716303, #10716318, C4×#5210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14645);