Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1361 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(5,8)(6,10)(13,17)(14,21)(15,22)(18,19)(20,26)(23,27)(24,25);(2,3)(4,5,6,9,7,8,10,11)(12,13)(14,17)(15,24)(16,20)(18,21)(19,22)(23,26)(25,27)Polycyclic presentation:
2^7,3|a^2=d,c^2=fg,d^2=efg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=defg,e^b=eg,f^b=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1361, C2×#67790, #10706429, … |
| maximal normal subgroup of | D3×#1361, C2×#67790, #10706429, … |
| maximal quotient of | #10681912, #10681918, #10681920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 366);