Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#944 |
| Sylow | C3 ⋊ C4×C4⋊Q8 |
588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(9,11)(12,14,15,19)(13,16,17,18);(12,13,15,17)(14,18,19,16);(2,3)(8,9,10,11);(4,5,6,7)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10689834, #10689835, #10689837, … |
| maximal normal subgroup of | #10689834, #10689835, #10689837, … |
| maximal quotient of | C4×#4976, C4×#5229, C4×#4973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15029);