Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2005 |
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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)(5,7)(8,11,13,10)(9,15,17,18)(12,19,22,20)(14,16,23,21);(1,2,3)(8,10,13,11)(9,14,17,23)(12,20,22,19)(15,21,18,16);(4,5)(6,7)(8,9)(10,18)(11,15)(12,21)(13,17)(14,19)(16,22)(20,23)Polycyclic presentation:
2^7,3|b^2=g,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,c^b=cf,d^b=dg,d^c=dg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2005, C2×#72108, #10822092, … |
| maximal normal subgroup of | D3×#2005, C2×#72108, #10822092, … |
| maximal quotient of | #10695401, #10695415, #10695457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4684);