Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #2012 |
426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(9,11)(12,13)(14,19)(15,17)(16,18);(2,3)(5,7)(8,9)(10,11)(12,13,15,17)(14,19,18,16);(2,3)(4,5)(6,7)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,h^b=h^2,d^c=dg,e^c=eg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2012, C2×#68675, #10822261, … |
| maximal normal subgroup of | D3×#2012, C2×#68675, #10822261, … |
| maximal quotient of | #10695617, #10695624, #10695638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1251);