Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #1438 |
1168 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(13,15)(17,19);(2,3)(9,11)(16,17)(18,19);(4,5,6,7)(8,9)(10,11)(12,13)(14,15)Polycyclic presentation:
2^7,3|a^2=g,b^a=bd,c^a=ce,c^b=cf,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10687756, D3×#1438, C2×#71550, … |
| maximal normal subgroup of | #10687756, D3×#1438, C2×#71550, … |
| maximal quotient of | #10683108, #10683109, #10683113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4126);