Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3079 |
416 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(12,14,16,15)(13,17,18,19);(12,13)(14,17)(15,19)(16,18);(4,6,7,11)(5,8,9,10);(2,3)(4,5,7,9)(6,10,11,8)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^2,f^c=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10691036, #10691038, #10691043, … |
| maximal normal subgroup of | #10691036, #10691038, #10691043, … |
| maximal quotient of | #10794682, #10796164, #10797372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15084);