Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#4649 |
| Sylow | C3 ⋊ C2×C4×C4⋊C4 |
928 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);(10,11,12,13)(14,16,17,15);(1,2)(4,5)(14,15,17,16);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684782, #10684794, #10685181, … |
| maximal normal subgroup of | #10684782, #10684794, #10685181, … |
| maximal quotient of | C2×Dic3×#95, C4×#4649, C2×#69402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5897);