Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×GL(2,𝔽3) |
| Fitting | Q82 ⋊ D3 |
255 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 16 points:
(9,10,16,11,12,15,14,13);(1,3,4,8)(2,5,6,7)(10,13,16)(11,14,15);(1,2,4,6)(3,7,8,5)40 conjugacy classes — view the full character table.
| maximal subgroup of | #11712301, #11712303, #11712304, … |
| maximal normal subgroup of | #11712301, #11712303, #11712304, … |
| maximal quotient of | Q8×#859, C4⋊C4×GL(2,𝔽3), #11713099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18005);