Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1330 |
100 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)(6,11)(9,10)(13,17)(14,20)(19,24)(21,26);(2,3)(4,5)(6,8)(7,10)(9,11)(12,13,14,18,16,19,21,25,15,17,20,23,22,24,26,27)Polycyclic presentation:
2^7,3|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^2,c^b=ceg,d^b=dg66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1330, C2×#67761, #10704904, … |
| maximal normal subgroup of | D3×#1330, C2×#67761, #10704904, … |
| maximal quotient of | #10681848, #10681851, #10681854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 337);