Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1693 |
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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 — 3 generators on 19 points:
(1,2,3)(5,8)(6,11)(9,10)(13,18)(16,19);(2,3)(12,13,17,19,15,18,14,16);(4,5,7,10)(6,8,11,9)(13,16)(14,17)(18,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=df,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^2,e^c=eg42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1693, C2×#71041, #10777724, … |
| maximal normal subgroup of | D3×#1693, C2×#71041, #10777724, … |
| maximal quotient of | #10688279, #10691394, #10691398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3617);