Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2150 |
172 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(9,13)(14,19)(15,20)(21,23);(4,5,6,7);(2,3)(5,7)(8,9,10,14,11,15,16,21,12,13,17,19,18,20,22,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682051, #10682052, #10682054, … |
| maximal normal subgroup of | #10682051, #10682052, #10682054, … |
| maximal quotient of | #10706732, #10706758, #10706791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2319);