Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#930 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C4×#121 |
824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,11);(12,13,14,15);(2,3)(8,9)(10,11)(13,15);(4,5,6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10683144, #10683147, #10683217, … |
| maximal normal subgroup of | #10683144, #10683147, #10683217, … |
| maximal quotient of | C4×#5213, C4×#4940, C4×#4939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14647);