Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1365 |
86 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)(4,5,7,9)(6,11,10,8)(13,18)(14,23)(15,25)(17,24)(19,21)(20,26)(22,27);(2,3)(5,8)(6,10)(9,11)(12,13,15,18,17,21,14,22,16,20,23,26,24,27,25,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=eg,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^2,c^b=cf,d^b=def,f^b=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1365, C2×#67802, #10706473, … |
| maximal normal subgroup of | D3×#1365, C2×#67802, #10706473, … |
| maximal quotient of | #10681978, #10682372, #10682847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 378);