Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1410 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(5,9)(6,13)(7,16)(10,12)(14,15)(17,18);(2,3)(4,5,6,11,8,12,15,19)(7,9,13,17,16,10,14,18)Polycyclic presentation:
2^7,3|a^2=d,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=cfg,d^b=def,e^b=eg,d^c=dfg,e^d=eg39 conjugacy classes — view the full character table.
| maximal subgroup of | #10683009, #10683010, #10683012, … |
| maximal normal subgroup of | #10683009, #10683010, #10683012, … |
| maximal quotient of | #10682570, #10682604, #10682700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 365);