Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67467 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#340 ⋊ C2 |
| Sylow | C3 ⋊ #1347 |
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 27 points:
(2,3)(4,6)(5,8)(7,11)(9,10)(13,17)(14,21)(15,22)(18,19)(20,26)(23,27)(24,25);(1,2,3)(4,5)(6,10,11,8)(7,9)(12,13)(14,17)(15,24)(16,20)(18,21)(19,22)(23,26)(25,27)Polycyclic presentation:
2^7,3|a^2=d,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1347, C2×#67485, #10705413, … |
| maximal normal subgroup of | D3×#1347, C2×#67485, #10705413, … |
| maximal quotient of | #10681859, #10681868, #10681895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 61);