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×#135 ⋊ C2 |
| Sylow | C3 ⋊ #3150 |
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 — 4 generators on 23 points:
(1,2,3)(8,11,13,12)(9,15,16,21)(10,19,18,20)(14,17,22,23);(2,3)(4,5,6,7)(10,18)(14,22)(17,23)(19,20);(8,10,12,20,13,18,11,19)(9,14,15,17,16,22,21,23);(5,7)(8,9)(10,17)(11,15)(12,21)(13,16)(14,20)(18,23)(19,22)Polycyclic presentation:
2^7,3|b^2=e,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10714109, #10714112, #10714114, … |
| maximal normal subgroup of | #10714109, #10714112, #10714114, … |
| maximal quotient of | #10782917, #10782918, #10782921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16480);