Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3124 |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(2,3)(4,6,7,10)(5,9,8,11)(14,22)(17,21)(23,27)(25,26);(1,2,3)(13,18)(16,24)(17,25)(19,20)(21,26)(23,27);(5,8)(9,11)(12,14,15,22)(13,17,19,21)(16,23,24,27)(18,25,20,26);(4,5)(6,9)(7,8)(10,11)(12,13)(14,21)(15,19)(16,18)(17,22)(20,24)(23,26)(25,27)Polycyclic presentation:
2^7,3|b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3124, C2×#80074, #11663547, … |
| maximal normal subgroup of | D3×#3124, C2×#80074, #11663547, … |
| maximal quotient of | #10795298, #10798268, #10798309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12650);