Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×SL(2,𝔽3)⋊C8 |
| derived | SL(2,𝔽3) ⋊ C2×C8 |
151 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 151 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 18 points:
(3,4,10,5,6,9,8,7)(11,12,13,15,14,16,17,18);(1,2)(4,7,10)(5,8,9)64 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SL(2,𝔽3)⋊C8, #11710987, #11710988, … |
| maximal normal subgroup of | C4×SL(2,𝔽3)⋊C8, #11710987, #11710988, … |
| maximal quotient of | C4×SL(2,𝔽3)⋊C8, #11711013, C4⋊(SL(2,𝔽3)⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5630);