Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#450 ⋊ C2 |
| Sylow | C3 ⋊ #3193 |
462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(13,16)(17,18);(6,11)(8,10)(13,17)(15,19)(16,18);(2,3)(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,h^b=h^2,f^c=fg45 conjugacy classes — view the full character table.
| maximal subgroup of | #10769304, #10769318, #10769372, … |
| maximal normal subgroup of | #10769304, #10769318, #10769372, … |
| maximal quotient of | #10804235, #10804243, #10805466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12728);