Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #3266 |
494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(10,17)(11,21)(13,22)(14,20)(16,23)(18,19);(5,7);(2,3)(8,10,12,19)(9,13,15,23)(11,17,21,18)(14,22,20,16);(4,5)(6,7)(8,9,12,15)(10,16,19,22)(11,20,21,14)(13,17,23,18)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^b=h^2,e^d=eg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3266, C2×#83506, #11670256, … |
| maximal normal subgroup of | D3×#3266, C2×#83506, #11670256, … |
| maximal quotient of | #10784560, #10784680, #10784815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16082);