Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3384 |
374 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)(4,7,8,5)(6,9,11,10);(12,13)(14,19)(15,17)(16,18);(4,6,8,11)(5,9,7,10)(13,17)(16,19);(2,3)(4,5,8,7)(6,10,11,9)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^b=de,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3384, C2×#79855, #11675752, … |
| maximal normal subgroup of | D3×#3384, C2×#79855, #11675752, … |
| maximal quotient of | #10811813, #10811824, #10813462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12431);