Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1281 |
152 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)(12,14,15,22,16,21,23,27)(13,17,19,24,18,20,25,26);(2,3)(4,5,6,8,7,9,10,11)(12,13)(14,20,21,17)(15,19)(16,18)(22,26,27,24)(23,25)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,h^a=h^2,d^b=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #10681945, #10681946, #10681990, … |
| maximal normal subgroup of | #10681945, #10681946, #10681990, … |
| maximal quotient of | #10681717, #10681721, #10681723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 237);