Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4513 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1368 |
68 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)(12,13,14,17,15,19,20,24,16,18,21,23,22,25,27,26);(2,3)(4,5,6,8,7,9,10,11)(13,17,18,23)(14,20)(15,22)(19,26,25,24)(21,27)Polycyclic presentation:
2^7,3|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,d^b=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10682655, #10682656, #10682857, … |
| maximal normal subgroup of | #10682655, #10682656, #10682857, … |
| maximal quotient of | #10681925, #10682061, #10682857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 89);