Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ #3004 |
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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)(9,14)(13,22)(15,19)(16,23);(5,7);(2,3)(8,10,12,18)(9,13,14,22)(11,20,21,17)(15,23,19,16);(4,5)(6,7)(8,9)(10,16)(11,19)(12,14)(13,17)(15,21)(18,23)(20,22)Polycyclic presentation:
2^7,3|b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10693204, #10693206, #10767590, … |
| maximal normal subgroup of | #10693204, #10693206, #10767590, … |
| maximal quotient of | #10767563, #10767602, #10767641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15509);