Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2241 |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3)(5,9)(8,11)(12,15,16,24,26,21,17,22,19,25,20,14,18,23,27,13);(4,6,7,10)(5,8,9,11)(12,14,17,15,18,22,16,23,19,24,27,25,26,13,20,21);(2,3)(4,5)(6,8)(7,9)(10,11)(12,13,19,22)(14,18,24,26)(15,17,25,27)(16,23,20,21)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #10708809, #10708810, #10708816, … |
| maximal normal subgroup of | #10708809, #10708810, #10708816, … |
| maximal quotient of | #10711567, #10713110, #10713405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1641);