Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1838 |
180 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)(12,15,16,25,18,24,17,14)(13,20,21,19,22,23,26,27);(2,3)(4,6,7,10)(5,8,9,11)(12,14,16,15,18,25,17,24)(13,19,21,23,22,27,26,20);(4,5)(6,8)(7,9)(10,11)(12,13,17,21,18,22,16,26)(14,23,24,27,25,20,15,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cg,h^b=h^2,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10682599, #10689582, #10689583, … |
| maximal normal subgroup of | #10682599, #10689582, #10689583, … |
| maximal quotient of | #10688853, #10688855, #10688857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3093);