Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1437 |
828 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(8,10,11,9)(17,19);(2,3)(4,5,6,7)(13,15);(8,9,11,10)(12,13)(14,15)(16,17,18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10682211, #10682213, #10686698, … |
| maximal normal subgroup of | #10682211, #10682213, #10686698, … |
| maximal quotient of | #10683106, #10683109, #10683111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4121);