Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2120 |
264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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:
(1,2,3)(4,6,8,13)(5,10,11,17)(7,12,15,19)(9,16,14,18);(5,9)(10,16)(11,14)(17,18);(2,3)(4,5)(6,10)(7,14,15,9)(8,11)(12,18,19,16)(13,17)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,e^b=ef,e^d=eg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10710339, #10710342, #10710344, … |
| maximal normal subgroup of | #10710339, #10710342, #10710344, … |
| maximal quotient of | #10704273, #10704362, #10704437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4292);