Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C3×D8 ⋊ C2 |
| Sylow | C3 ⋊ #3008 |
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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 — 4 generators on 23 points:
(1,2,3)(10,17)(14,21)(18,23)(20,22);(2,3)(5,7)(8,10)(9,14)(11,18)(12,17)(13,20)(15,22)(16,21)(19,23);(9,13)(11,19)(14,20)(15,16)(18,23)(21,22);(4,5)(6,7)(8,9)(10,14)(11,13)(12,16)(15,19)(17,21)(18,20)(22,23)Polycyclic presentation:
2^7,3|e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10826707, #10826709, #10832569, … |
| maximal normal subgroup of | #10826707, #10826709, #10832569, … |
| maximal quotient of | #10768343, #10768431, #10768519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16409);