Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#914 |
| Fitting | C3×C4×SD16 ⋊ 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)(8,9,11,12)(10,15,14,13);(9,13)(10,14)(12,15);(2,3)(9,12)(13,15);(4,5,6,7)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10764598, C8×#914, #10764620, … |
| maximal normal subgroup of | #10764598, C8×#914, #10764620, … |
| maximal quotient of | C8×#914, #10764771, #10764791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12221);