Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4⋊C4×D12 |
| Fitting | C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ D4×C4⋊C4 |
776 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)(12,13,14,15);(2,3)(13,15);(8,9,10,11);(4,5,6,7)(9,11)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10689346, #10689350, #10689374, … |
| maximal normal subgroup of | #10689346, #10689350, #10689374, … |
| maximal quotient of | C4⋊C4×(C2×D3)⋊C4, C4⋊C4×C4⋊Dic3, D12×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6345);