Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1352 |
154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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)(5,8,10,9)(12,13)(14,18)(15,17)(16,19);(2,3)(4,5)(6,9,11,8)(7,10)(13,16,17,18)Polycyclic presentation:
2^7,3|a^2=d,b^2=eg,c^2=fg,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,d^b=defg,h^b=h^2,d^c=dg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1352, C2×#67451, #10705464, … |
| maximal normal subgroup of | D3×#1352, C2×#67451, #10705464, … |
| maximal quotient of | #10681985, #10682006, #10682308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 27);