Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#882 |
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C4×#120 |
1224 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,11)(12,13,14,15);(8,9)(10,11);(2,3)(13,15);(4,5,6,7)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10689871, #10689881, #10800681, … |
| maximal normal subgroup of | #10689871, #10689881, #10800681, … |
| maximal quotient of | C4×#4665, C4×#4958, C4×#4950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6140);