Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#104 |
| Fitting | C2×C3×#104 ⋊ C2 |
| Sylow | C3 ⋊ C22×#104 |
856 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 13 points:
(3,4,5)(6,7)(8,11)(9,12)(10,13);(6,7,8,11,9,12,13,10);(1,2)(4,5);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#104, D3×#1759, #10792914, … |
| maximal normal subgroup of | C4×D3×#104, D3×#1759, #10792914, … |
| maximal quotient of | C2×D3×D4⋊C8, C2×D3×Q8⋊C8, D3×#1476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11557);