Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1841 |
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,7,14,8,15,16,18)(5,10,11,13,12,19,9,17);(2,3)(5,9,12,11)(10,17,19,13);(4,5)(6,13,15,17)(7,9)(8,12)(10,18,19,14)(11,16)Polycyclic presentation:
2^7,3|a^2=f,b^2=deg,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ceg,d^a=dg,h^b=h^2,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10706025, #10706027, #10706032, … |
| maximal normal subgroup of | #10706025, #10706027, #10706032, … |
| maximal quotient of | #10688905, #10688909, #10688913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1272);