Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ #3058 |
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 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) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(10,17)(15,22)(18,21)(19,23);(5,7)(8,10)(9,15)(11,18)(12,17)(13,19)(14,21)(16,22)(20,23);(8,9,14,20,12,16,11,13)(10,15,21,23,17,22,18,19);(2,3)(4,5)(6,7)(9,13)(11,14)(15,19)(16,20)(18,21)(22,23)Polycyclic presentation:
2^7,3|b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,d^c=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10706180, #10706182, #10706188, … |
| maximal normal subgroup of | #10706180, #10706182, #10706188, … |
| maximal quotient of | #10778258, #10778297, #10778345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16375);