Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#468 ⋊ C2 |
| Sylow | C3 ⋊ #3193 |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,3)(5,9)(8,10)(13,16)(17,18);(1,2,3)(6,11)(8,10)(13,17)(15,19)(16,18);(4,6)(5,8)(7,11)(9,10)(13,16)(17,18);(4,5)(6,10)(7,9)(8,11)(12,13,14,16)(15,17,19,18)Polycyclic presentation:
2^7,3|a^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^d=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3193, C2×#80811, #11665822, … |
| maximal normal subgroup of | D3×#3193, C2×#80811, #11665822, … |
| maximal quotient of | #10804233, #10804240, #10805469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13387);