Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67467 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1363 |
80 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)(4,5,7,9)(6,11,10,8)(12,14,17,24)(13,19,21,18)(15,25,16,20)(22,27,26,23);(2,3)(5,8)(6,10)(9,11)(12,13,16,20,19,24,26,27,17,21,15,25,18,14,22,23)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,d^2=ef,f^2=g,b^a=bc,c^a=ce,h^a=h^2,c^b=cf,d^b=def,f^b=fg,h^b=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1363, C2×#67468, #10706451, … |
| maximal normal subgroup of | D3×#1363, C2×#67468, #10706451, … |
| maximal quotient of | #10681976, #10681979, #10682377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 44);