Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#519 ⋊ C2 |
| Sylow | C3 ⋊ #2947 |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(10,16)(14,21)(17,22)(20,23);(4,6,7,5)(8,10)(9,14)(11,17)(12,16)(13,20)(15,21)(18,22)(19,23);(8,9,12,15)(10,14,16,21)(11,19,18,13)(17,23,22,20);(2,3)(4,5,7,6)(9,13)(11,18)(14,20)(15,19)(17,22)(21,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,e^a=eg,h^a=h^2,e^b=eg,d^c=dg78 conjugacy classes — view the full character table.
| maximal subgroup of | #10815978, #10815984, #10815996, … |
| maximal normal subgroup of | #10815978, #10815984, #10815996, … |
| maximal quotient of | #10764636, #10764827, #10764844, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15123);