Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3120 |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2)(4,6,7,10)(5,9,8,11)(14,21)(17,25)(22,27)(24,26);(13,18)(15,23)(17,24)(19,20)(22,27)(25,26);(5,8)(9,11)(12,14,16,21)(13,17,20,25)(15,22,23,27)(18,24,19,26);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13,16,20)(14,17,21,25)(15,18,23,19)(22,24,27,26)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^b=dg,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3120, C2×#80217, #11663547, … |
| maximal normal subgroup of | D3×#3120, C2×#80217, #11663547, … |
| maximal quotient of | #10795298, #10798264, #10798286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12793);