Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C3×#117 ⋊ C2 |
| Sylow | C3 ⋊ #1899 |
378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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)(5,7)(8,11,12,18)(9,14,15,21)(10,16,17,22)(13,19,20,23);(8,10)(9,13,15,20)(11,16)(12,17)(14,19,21,23)(18,22);(2,3)(4,5)(6,7)(8,9)(10,13,17,20)(11,14)(12,15)(16,19,22,23)(18,21)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,d^b=dg,f^b=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10687513, #10687515, #10687520, … |
| maximal normal subgroup of | #10687513, #10687515, #10687520, … |
| maximal quotient of | #10690563, #10690573, #10690583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4171);