Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68807 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ #2014 |
474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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:
(1,2,3)(9,11)(13,18)(14,15)(17,19);(2,3)(5,7)(8,9)(10,11)(13,17)(14,15)(18,19);(4,5)(6,7)(12,13,16,19)(14,17,15,18)Polycyclic presentation:
2^7,3|a^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,e^b=eg,h^b=h^2,d^c=dg,e^c=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2014, C2×#72056, #10822254, … |
| maximal normal subgroup of | D3×#2014, C2×#72056, #10822254, … |
| maximal quotient of | #10695660, #10695661, #10695702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4632);