Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#5212 |
| Sylow | C3 ⋊ C2×#380 |
1232 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(6,7)(8,9)(14,15)(16,17);(1,2)(10,11,12,13);(4,5)(7,9)(11,13)(14,15,16,17);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684806, #10684808, C2×#67625, … |
| maximal normal subgroup of | #10684806, #10684808, C2×#67625, … |
| maximal quotient of | C2×#72127, C2×#71534, C2×#71535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16601);