Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×#67⋊C4 |
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C42×D4 |
924 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)(8,9,10,11)(13,15);(12,13)(14,15);(2,3)(13,15);(4,5,6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#67⋊C4, #10793530, #10793535, … |
| maximal normal subgroup of | C8×#67⋊C4, #10793530, #10793535, … |
| maximal quotient of | C4×#4666, C4×Dic3×C22⋊C4, C4×#4649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6010);