Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1380 |
152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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) = 384 |
A minimal faithful permutation representation — 2 generators on 27 points:
(2,3)(8,9,10,11)(12,13,15,19,16,20,14,18,17,21,22,26,23,25,24,27);(1,2,3)(4,5,6,7)(13,18)(14,22)(15,24)(16,23)(19,20)(21,27)(25,26)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1380, C2×#67722, #10710065, … |
| maximal normal subgroup of | D3×#1380, C2×#67722, #10710065, … |
| maximal quotient of | #10682056, #10682101, #10682103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 298);