Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#441 ⋊ 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)(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=dg,h^d=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2947, C2×#79830, #11659303, … |
| maximal normal subgroup of | D3×#2947, C2×#79830, #11659303, … |
| maximal quotient of | #10764635, #10764826, #10764845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12406);