Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #1784 |
564 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 133 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:
(1,2,3)(5,7);(8,10,12,18)(9,13,14,16)(11,19,20,17)(15,23,22,21);(2,3)(4,5)(6,7)(8,9,11,15,12,14,20,22)(10,16,17,23,18,13,19,21)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10682467, #10682468, #10682484, … |
| maximal normal subgroup of | #10682467, #10682468, #10682484, … |
| maximal quotient of | #10686517, #10686531, #10686541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4709);