Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ C4×#137 |
484 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)(9,14)(13,22)(15,19)(16,23);(2,3)(4,6,7,5);(2,3)(8,10,12,18)(9,13,14,22)(11,20,21,17)(15,23,19,16);(2,3)(4,5,7,6)(8,9)(10,16)(11,19)(12,14)(13,17)(15,21)(18,23)(20,22)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,h^b=h^2,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10801067, #10801069, #10801089, … |
| maximal normal subgroup of | #10801067, #10801069, #10801089, … |
| maximal quotient of | #10764617, #10764786, #10764799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11443);