Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1817 |
380 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 149 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) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(5,7)(16,18,19,22)(17,21,20,23);(17,20)(21,23);(2,3)(4,5)(6,7)(8,9,10,12,11,13,14,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10681718, #10681719, #10681727, … |
| maximal normal subgroup of | #10681718, #10681719, #10681727, … |
| maximal quotient of | #10688510, #10688513, #10688516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4107);