Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1313 |
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)(4,5,6,8,7,9,10,11)(13,17,19,20)(14,21)(18,26,27,25)(22,24);(2,3)(12,13,14,18,15,20,22,26,16,19,21,27,23,17,24,25)Polycyclic presentation:
2^7,3|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^2,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1313, C2×#67512, #10704186, … |
| maximal normal subgroup of | D3×#1313, C2×#67512, #10704186, … |
| maximal quotient of | #10681804, #10682016, #10682524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 88);