Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4⋊C4×#67 |
| Fitting | C22×C3×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)(13,15);(2,3)(12,13)(14,15);(8,9,10,11);(4,5,6,7)(9,11)90 conjugacy classes — view the full character table.
| maximal subgroup of | #67×#102, #10810591, #67×#103, … |
| maximal normal subgroup of | #67×#102, #10810591, #67×#103, … |
| maximal quotient of | C4⋊C4×(C2×D3)⋊C4, C4⋊C4×#217, C4⋊C4×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14763);