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×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #2973 |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(5,9)(8,10);(2,3)(6,11)(8,10)(13,16)(17,19);(4,6)(5,8)(7,11)(9,10);(4,5)(6,10)(7,9)(8,11)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^7,3|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10689156, #10689159, #10689879, … |
| maximal normal subgroup of | #10689156, #10689159, #10689879, … |
| maximal quotient of | #10793862, #10793876, #10793920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11178);