Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1334 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(12,13,16,18)(14,21,22,26)(15,24,23,19)(17,20,25,27);(2,3)(4,5,6,8,7,9,10,11)(13,17,18,25)(14,20)(15,23)(19,21,24,26)(22,27)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=ceg,d^b=dg,e^b=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1334, C2×#67764, #10704952, … |
| maximal normal subgroup of | D3×#1334, C2×#67764, #10704952, … |
| maximal quotient of | #10681845, #10681857, #10681957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 340);