Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #2316 |
600 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 309 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)(13,17)(16,18);(8,9,10,11)(14,19)(16,18);(12,14,15,19)(13,16,17,18);(2,3)(4,5,6,7)(9,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | #10688721, #10689179, #10689182, … |
| maximal normal subgroup of | #10688721, #10689179, #10689182, … |
| maximal quotient of | #10716444, #10716480, #10716577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14732);