Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2040 |
290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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 — 3 generators on 23 points:
(2,3)(4,6,7,5)(9,15)(10,19)(12,13)(16,17)(20,21)(22,23);(1,2,3)(4,5)(6,7)(8,10)(9,14)(11,20)(12,21)(13,19)(15,23)(16,18)(17,22);(5,6)(8,9)(10,18)(11,16)(12,15)(13,17)(14,20)(19,23)(21,22)Polycyclic presentation:
2^7,3|c^2=dg,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,f^b=fg,e^c=eg,f^c=fg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10707515, #10707517, #10707529, … |
| maximal normal subgroup of | #10707515, #10707517, #10707529, … |
| maximal quotient of | #10698513, #10698518, #10698537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4453);