Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67467 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1364 |
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)(4,5,7,9)(6,11,10,8)(13,17)(14,21)(15,22)(18,19)(20,25)(23,27)(24,26);(2,3)(5,8)(6,10)(9,11)(12,13,14,18,22,26,27,25,16,20,23,24,15,19,21,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,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=fg,h^b=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1364, C2×#67475, #10706473, … |
| maximal normal subgroup of | D3×#1364, C2×#67475, #10706473, … |
| maximal quotient of | #10681976, #10682374, #10682839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 51);