Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#932 |
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ C4×AGL(1,ℤ/8) |
548 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)(9,14)(10,11)(13,15);(8,10,12,11)(9,13,15,14);(2,3)(8,9)(10,13)(11,14)(12,15);(4,5,6,7)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10689808, #10689814, #10689822, … |
| maximal normal subgroup of | #10689808, #10689814, #10689822, … |
| maximal quotient of | C8×#932, #10764770, #10764790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14868);