Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#137 ⋊ C2 |
| Sylow | C3 ⋊ #3271 |
488 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)(8,11,13,19)(9,15,16,23)(10,17,12,21)(14,22,20,18);(2,3)(5,7)(8,10,13,12)(9,14,16,20)(11,17,19,21)(15,22,23,18);(8,9,13,16)(10,14,12,20)(11,18,19,22)(15,21,23,17);(4,5)(6,7)(9,14)(10,12)(15,22)(16,20)(17,21)(18,23)Polycyclic presentation:
2^7,3|b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^c=h^2,e^d=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3271, C2×#83990, #11670259, … |
| maximal normal subgroup of | D3×#3271, C2×#83990, #11670259, … |
| maximal quotient of | #10784633, #10784753, #10784978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16566);