Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #2989 |
388 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)(4,6,7,10)(5,9,8,11);(2,3)(5,8)(9,11)(13,16)(17,19);(4,5)(6,9)(7,8)(10,11);(2,3)(5,8)(6,10)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^7,3|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^2,c^b=ce,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10689083, #10689087, #10689090, … |
| maximal normal subgroup of | #10689083, #10689087, #10689090, … |
| maximal quotient of | #10794006, #10794019, #10794084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11590);