Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#127 ⋊ C2 |
| Sylow | C3 ⋊ #2002 |
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(5,7)(10,15)(12,13);(9,12)(10,15)(13,14);(2,3)(4,5)(6,7)(8,9)(10,12)(11,14)(13,15)Polycyclic presentation:
2^7,3|d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2002, C2×#71769, #10822091, … |
| maximal normal subgroup of | D3×#2002, C2×#71769, #10822091, … |
| maximal quotient of | #10695383, #10695425, #10695439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4345);