Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ #2019 |
362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(9,14)(10,18)(11,21)(15,16)(17,22)(19,20);(2,3)(5,7)(8,10)(9,13)(11,18)(12,20)(14,17)(15,22)(16,23)(19,21);(2,3)(4,5)(6,7)(8,9,12,16)(10,17,20,22)(11,14,21,15)(13,18,23,19)Polycyclic presentation:
2^7,3|a^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,f^b=fg,h^b=h^2,d^c=dg,e^c=eg,f^c=fg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2019, C2×#70091, #10822389, … |
| maximal normal subgroup of | D3×#2019, C2×#70091, #10822389, … |
| maximal quotient of | #10695794, #10695811, #10695861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2667);