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 ⋊ #3077 |
440 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)(13,17)(16,18);(13,16)(14,19)(17,18);(2,3)(4,6,7,11)(5,8,9,10);(4,5,7,9)(6,10,11,8)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^2,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3077, C2×#81166, #11662729, … |
| maximal normal subgroup of | D3×#3077, C2×#81166, #11662729, … |
| maximal quotient of | #10794666, #10796139, #10796144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13742);