Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2024 |
290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(5,7)(16,17,19,21)(18,23,22,20);(1,2,3)(4,5)(6,7)(8,10,11,15)(9,12,13,14);(8,9,11,13)(10,14,15,12)(17,20)(18,22)(21,23)Polycyclic presentation:
2^7,3|a^2=d,b^2=d,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,e^c=eg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10683989, #10683991, #10684001, … |
| maximal normal subgroup of | #10683989, #10683991, #10684001, … |
| maximal quotient of | #10698159, #10698169, #10698199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4370);