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 ⋊ #3277 |
476 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)(8,10,12,18)(9,15,14,23)(11,21,19,17)(13,22,20,16);(5,7)(9,14)(13,20)(15,23)(16,22);(8,9,12,14)(10,16,18,22)(11,20,19,13)(15,21,23,17);(2,3)(4,5)(6,7)(9,13)(11,19)(14,20)(15,22)(16,23)(17,21)Polycyclic presentation:
2^7,3|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,c^b=cg,d^b=de,e^b=eg,e^d=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3277, C2×#83994, #11670362, … |
| maximal normal subgroup of | D3×#3277, C2×#83994, #11670362, … |
| maximal quotient of | #10786505, #10786615, #10786621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16570);