Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#342 ⋊ C2 |
| Sylow | C3 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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:
(2,3)(4,6,7,5);(1,2,3)(8,10)(9,12,13,14)(11,15);(4,5,7,6)(8,9)(10,14)(11,13)(12,15)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=e,b^a=bd,f^a=fg,d^b=dg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10705508, #10705510, #10705513, … |
| maximal normal subgroup of | #10705508, #10705510, #10705513, … |
| maximal quotient of | #10685688, #10685692, #10685696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1528);