Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#4989 |
| Fitting | C22×C3×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#385 |
1232 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,7,8,9)(10,11)(12,13);(1,2)(10,11,12,13)(15,17);(1,2)(4,5)(14,15)(16,17);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10690565, #10690585, C4×#4989, … |
| maximal normal subgroup of | #10690565, #10690585, C4×#4989, … |
| maximal quotient of | C2×(C2×D3)⋊#95, C2×#69406, C2×#71564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14761);