Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | M16×#67 |
| Fitting | C22×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(5,7);(2,3)(4,5)(6,7);(9,12)(13,15);(8,9,10,13,11,12,14,15)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10810534, #67×#100, #10810542, … |
| maximal normal subgroup of | #10810534, #67×#100, #10810542, … |
| maximal quotient of | M16×#213, #10766615, M16×#214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16334);