Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67645 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1354 |
140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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) = 96 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,6,7,11)(5,8)(12,13)(14,18)(15,17)(16,19);(2,3)(4,5,6,10,7,8,11,9)(13,16,17,18)Polycyclic presentation:
2^7,3|a^2=d,b^2=eg,c^2=fg,d^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,d^b=defg,d^c=dg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1354, C2×#67648, #10705492, … |
| maximal normal subgroup of | D3×#1354, C2×#67648, #10705492, … |
| maximal quotient of | #10681984, #10682005, #10682309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 224);