Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1290 |
136 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)(12,14,16,24,17,23,15,22)(13,18,19,21,20,26,25,27);(2,3)(4,5,6,9,7,8,10,11)(12,13)(14,21,23,27)(15,19)(16,25)(17,20)(18,22,26,24)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^2,d^b=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10681872, #10681873, #10681875, … |
| maximal normal subgroup of | #10681872, #10681873, #10681875, … |
| maximal quotient of | #10681725, #10681733, #10681774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 284);