Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#568⋊C3 |
| unambiguous semidirect product | (C2×#568)⋊C3 |
| Fitting, Sylow | C2×#568 ⋊ C3 |
345 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 34 points:
(3,4,5,10,8,9,15,20)(6,12,27,23,19,26,28,32,16,11,14,33,17,22,29,31,7,25,13,24,18,21,30,34);(1,2)(3,16,8,18)(4,26,9,25)(5,27,15,29)(6,19,17,7)(10,34,20,33)(11,12,21,22)(13,30,28,14)(23,24,31,32);(1,2)76 conjugacy classes — view the full character table.
| maximal subgroup of | #20338⋊C3, #11709426, #20343⋊C3, … |
| maximal normal subgroup of | #20338⋊C3, #11709426, #20343⋊C3, … |
| maximal quotient of | C2×#2875⋊C3, C4×#568⋊C3, C2×#2880⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18204);