Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2023 |
326 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 93 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 — 3 generators on 23 points:
(1,2,3)(5,7)(17,20)(18,23)(21,22);(4,5)(6,7)(8,10,11,15)(9,12,13,14);(2,3)(8,9,11,13)(10,14,15,12)(16,17)(18,20)(19,22)(21,23)Polycyclic presentation:
2^7,3|a^2=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,e^c=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10683974, #10683976, #10683985, … |
| maximal normal subgroup of | #10683974, #10683976, #10683985, … |
| maximal quotient of | #10698157, #10698167, #10698197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2214);