Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2007 |
370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 370 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:
(1,2,3)(5,7)(8,10)(9,14)(11,19)(12,21)(13,20)(15,18)(16,23)(17,22);(4,5)(6,7)(8,10)(9,14)(11,21)(12,19)(13,20)(15,23)(16,18)(17,22);(2,3)(8,9,13,17)(10,18,20,23)(11,16,12,15)(14,21,22,19)Polycyclic presentation:
2^7,3|a^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,c^b=cf,d^b=dg,e^c=eg48 conjugacy classes — view the full character table.
| maximal subgroup of | #10707258, #10707260, #10707272, … |
| maximal normal subgroup of | #10707258, #10707260, #10707272, … |
| maximal quotient of | #10695523, #10695530, #10695537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4457);