Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#450 ⋊ C2 |
| Sylow | C3 ⋊ #3208 |
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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);(6,11)(8,10)(13,16)(14,19)(17,18);(2,3)(4,6,7,11)(5,8,9,10);(4,5)(6,10)(7,9)(8,11)(12,13,15,18)(14,16,19,17)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^2,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10769168, #10769170, #10769182, … |
| maximal normal subgroup of | #10769168, #10769170, #10769182, … |
| maximal quotient of | #10804490, #10804866, #10805698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12714);