Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1380 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(8,9,10,11)(12,13,15,19,16,20,14,18,17,21,22,26,23,25,24,27);(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^a=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10682742, #10682743, #10682745, … |
| maximal normal subgroup of | #10682742, #10682743, #10682745, … |
| maximal quotient of | #10682057, #10682102, #10682224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 382);