Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#470 ⋊ C2 |
| Sylow | C3 ⋊ #3331 |
388 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)(6,11)(8,10)(12,15,16,17)(13,19,20,21)(14,24,23,25)(18,22,26,27);(2,3)(12,14)(13,18)(15,24)(16,23)(17,25)(19,22)(20,26)(21,27);(2,3)(4,6)(5,8)(7,11)(9,10)(14,23)(18,26)(22,27)(24,25);(2,3)(4,5,7,9)(6,10,11,8)(12,13,16,20)(14,22,23,27)(15,21,17,19)(18,25,26,24)Polycyclic presentation:
2^7,3|a^2=e,d^2=g,f^2=g,b^a=beg,c^a=cf,d^a=dg,f^a=fg,h^a=h^2,c^b=cg,d^b=deg,h^b=h^2,f^c=fg,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3331, C2×#80925, #11672141, … |
| maximal normal subgroup of | D3×#3331, C2×#80925, #11672141, … |
| maximal quotient of | #10810834, #10811631, #10812413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13501);