Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #1964 |
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(4,5,6,7);(8,10)(9,12,13,15)(11,14);(2,3)(5,7)(8,9)(10,12,14,15)(11,13)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=e,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,d^b=dg,f^b=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10687373, #10687375, #10687380, … |
| maximal normal subgroup of | #10687373, #10687375, #10687380, … |
| maximal quotient of | #10694011, #10694015, #10694020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2032);