Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68807 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ #2036 |
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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)(5,7)(8,10,11,9)(13,17)(15,19)(16,18);(2,3)(4,5)(6,7)(8,9)(10,11)(13,16)(17,18);(2,3)(9,10)(12,13,14,16)(15,17,19,18)Polycyclic presentation:
2^7,3|a^2=g,c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,h^b=h^2,e^c=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2036, C2×#70635, #10822663, … |
| maximal normal subgroup of | D3×#2036, C2×#70635, #10822663, … |
| maximal quotient of | #10698492, #10698499, #10698582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3211);