Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C3×Q16 ⋊ C2 |
| Sylow | C3 ⋊ #3270 |
472 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)(9,14,15,23)(11,21,19,17)(13,22,20,16);(5,7);(8,9,12,15)(10,16,18,22)(11,20,19,13)(14,21,23,17);(2,3)(4,5)(6,7)(9,13)(11,19)(14,22)(15,20)(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,d^b=de,e^b=eg,e^d=eg57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3270, C2×#83888, #11670265, … |
| maximal normal subgroup of | D3×#3270, C2×#83888, #11670265, … |
| maximal quotient of | #10784624, #10784744, #10784924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16464);