Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4972 |
| 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:
(3,4,5)(6,7)(8,9)(11,13)(14,16,17,15);(1,2)(10,11,12,13);(1,2)(4,5)(7,9)(14,15,17,16);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10701173, #10701178, #10701197, … |
| maximal normal subgroup of | #10701173, #10701178, #10701197, … |
| maximal quotient of | C2×#71563, C2×#69406, C4×#4972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14726);