Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#478 ⋊ C2 |
| Sylow | C3 ⋊ #3368 |
382 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)(4,6,7,11)(5,9,8,10);(2,3)(12,13,15,17)(14,19,18,16);(4,5,7,8)(6,10,11,9)(13,17)(16,19);(2,3)(5,8)(9,10)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^b=de,f^c=fg,h^c=h^2,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3368, C2×#81153, #11675006, … |
| maximal normal subgroup of | D3×#3368, C2×#81153, #11675006, … |
| maximal quotient of | #10811837, #10812018, #10814156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13729);