Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×C4⋊Q8 |
| Fitting | C2×C3×C4⋊Q8 ⋊ C2 |
| Sylow | C3 ⋊ C22×C4⋊Q8 |
1624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 17 points:
(3,4,5)(6,7,8,9);(1,2)(10,12,13,17)(11,14,15,16);(7,9)(10,11,13,15)(12,16,17,14);(4,5);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10686672, #10686681, #10710694, … |
| maximal normal subgroup of | #10686672, #10686681, #10710694, … |
| maximal quotient of | C2×D3×#384, C2×D3×#389, C2×D3×#391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18782);