Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#431 ⋊ C2 |
| Sylow | C3 ⋊ C8×#41 |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(12,14,15,18)(13,17,16,19);(2,3)(4,6,7,11,8,5,9,10);(13,16)(17,19);(4,5,7,10,8,6,9,11)(12,13)(14,17)(15,16)(18,19)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^c=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685892, #10685894, #10685899, … |
| maximal normal subgroup of | #10685892, #10685894, #10685899, … |
| maximal quotient of | #10793388, #10793393, C4×#67⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11852);