Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #2196 |
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(3,7)(9,10,11);(2,5)(6,8)(10,11);(1,2)(3,5)(4,6)(7,8)Polycyclic presentation:
2^7,3|b^a=bd,c^a=ce,f^a=fg,e^b=efg,h^b=h^2,d^c=df,e^d=eg36 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2196, C2×#70996, #10949206, … |
| maximal normal subgroup of | D3×#2196, C2×#70996, #10949206, … |
| maximal quotient of | #10707214, #10707215, #10707248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3572);