Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2244 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2)(5,9)(8,11)(12,14,15,13,20,19,27,23,18,25,26,22,17,24,16,21);(2,3)(4,6,7,10)(5,8,9,11)(12,13,16,14,17,21,26,24,18,22,27,25,20,23,15,19);(4,5)(6,8)(7,9)(10,11)(13,19)(14,23)(15,16)(17,20)(21,25)(22,24)(26,27)Polycyclic presentation:
2^7,3|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ceg,d^a=df,e^a=efg,f^a=fg,c^b=cg,h^b=h^2,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10708833, #10708834, #10708840, … |
| maximal normal subgroup of | #10708833, #10708834, #10708840, … |
| maximal quotient of | #10711574, #10713120, #10713420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3865);