Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1276 |
208 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(13,16,18,17);(2,3)(4,5,6,8,7,9,10,11)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10681938, #10681939, #10682010, … |
| maximal normal subgroup of | #10681938, #10681939, #10682010, … |
| maximal quotient of | #10681715, #10681719, #10681723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 187);