Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C3 ⋊ #1744 |
296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(16,18,19,22)(17,21,20,23);(4,5,6,7)(17,20)(21,23);(2,3)(8,9,10,12,11,13,14,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^2144 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊#7014, #10681720, #10681742, … |
| maximal normal subgroup of | C3⋊#7014, #10681720, #10681742, … |
| maximal quotient of | #10685610, #10685612, #10685616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1964);