Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2165 |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,10,9,12)(6,13)(11,19,16,18)(14,17);(5,9)(6,13)(10,12)(14,17);(2,3)(4,5,6,11,7,12,14,19,8,9,13,16,15,10,17,18)Polycyclic presentation:
2^7,3|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^2,e^b=eg,e^c=eg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10682247, #10682248, #10682250, … |
| maximal normal subgroup of | #10682247, #10682248, #10682250, … |
| maximal quotient of | #10710203, #10710253, #10710521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2440);