Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4928 |
| Sylow | C3 ⋊ C2×#389 |
800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(6,7,8,9)(15,17);(1,2)(10,11,12,13);(4,5)(11,13)(14,15,16,17);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67477, C2×#67478, #10683175, … |
| maximal normal subgroup of | C2×#67477, C2×#67478, #10683175, … |
| maximal quotient of | C2×#71535, C2×#71536, C4×#4928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14642);