Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#4940 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C2×#388 |
928 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,7,8,9)(14,16,17,15);(1,2)(10,11)(12,13)(14,15,17,16);(1,2)(4,5)(11,13)(15,16);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685711, #10685713, #10687857, … |
| maximal normal subgroup of | #10685711, #10685713, #10687857, … |
| maximal quotient of | C2×#71534, C2×#71536, C2×#71537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14640);