Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1462 |
440 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 93 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)(13,16)(17,19);(4,6)(5,8)(7,11)(9,10);(2,3)(4,5)(6,10,11,8)(7,9)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^7,3|a^2=e,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^2,e^b=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | #10682211, #10682212, #10682504, … |
| maximal normal subgroup of | #10682211, #10682212, #10682504, … |
| maximal quotient of | #10683318, #10683331, #10683345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4115);