Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #548⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×#557⋊C3 |
| unambiguous semidirect product | (C2×#557)⋊C3 |
| Fitting, Sylow | C2×#557 ⋊ C3 |
283 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 283 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2)(3,5,6,10)(4,7,8,9)(11,12,15,18)(13,17,21,24,14,23,20,26,19,16,22,25);(3,4,6,8)(5,9,10,7)(11,19,15,21)(12,23,18,25)(13,22,20,14)(16,26,24,17);(1,2)70 conjugacy classes — view the full character table.
| maximal subgroup of | #17430⋊C3, #22538⋊C3, #22542⋊C3, … |
| maximal normal subgroup of | #17430⋊C3, #22538⋊C3, #22542⋊C3, … |
| maximal quotient of | C2×C4⋊C4×SL(2,𝔽3), C2×#2351⋊C3, C4×#557⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18174);