Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#346 ⋊ C2 |
| Sylow | C3 ⋊ #1333 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2)(13,17)(14,23)(15,26)(18,19)(20,27)(21,22)(24,25);(2,3)(4,5,6,8,7,9,10,11)(12,13,15,19,16,21,26,20)(14,22,24,18,25,17,23,27)Polycyclic presentation:
2^7,3|a^2=d,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=ceg,d^b=dg,e^b=eg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1333, C2×#67516, #10704952, … |
| maximal normal subgroup of | D3×#1333, C2×#67516, #10704952, … |
| maximal quotient of | #10681843, #10681855, #10681955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 92);