Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#542 ⋊ C2 |
| Sylow | C3 ⋊ #3175 |
362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(13,18)(17,25)(19,24)(23,27);(2,3)(12,14,21,26,16,22,15,20)(13,17,24,27,18,25,19,23);(5,8)(9,11)(12,13)(14,17)(15,19)(16,18)(20,23)(21,24)(22,25)(26,27);(4,5)(6,9)(7,8)(10,11)(14,20)(15,21)(17,23)(19,24)(22,26)(25,27)Polycyclic presentation:
2^7,3|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3175, C2×#83457, #11665033, … |
| maximal normal subgroup of | D3×#3175, C2×#83457, #11665033, … |
| maximal quotient of | #10795753, #10799455, #10799463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16033);