Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#488 ⋊ C2 |
| Sylow | C3 ⋊ #3327 |
380 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)(6,11)(8,10)(13,18)(17,26)(19,24)(20,27);(2,3)(12,14,15,21)(13,17,18,26)(16,25,23,22)(19,27,24,20);(2,3)(4,6)(5,8)(7,11)(9,10)(14,21)(17,26)(20,27)(22,25);(4,5,7,9)(6,10,11,8)(12,13,15,18)(14,20,21,27)(16,24,23,19)(17,25,26,22)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,f^2=g,b^a=beg,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=deg,h^b=h^2,f^c=fg,h^c=h^2,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3327, C2×#81659, #11672136, … |
| maximal normal subgroup of | D3×#3327, C2×#81659, #11672136, … |
| maximal quotient of | #10810812, #10811594, #10812490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14235);