Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ #3154 |
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) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(10,16)(14,21)(17,22)(19,23);(2,3)(4,5,6,7)(8,10)(9,14)(11,17)(12,16)(13,19)(15,21)(18,22)(20,23);(8,9,11,13,12,15,18,20)(10,14,17,19,16,21,22,23);(5,7)(9,13)(11,18)(14,19)(15,20)(17,22)(21,23)Polycyclic presentation:
2^7,3|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10809086, #10809098, #10846648, … |
| maximal normal subgroup of | #10809086, #10809098, #10846648, … |
| maximal quotient of | #10783026, #10783037, #10783070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16430);