Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#532 ⋊ C2 |
| Sylow | C3 ⋊ #3147 |
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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 — 4 generators on 23 points:
(1,2,3)(8,11,13,12)(9,15,16,21)(10,18,20,19)(14,17,22,23);(4,5,6,7);(2,3)(8,10,12,19,13,20,11,18)(9,14,15,17,16,22,21,23);(5,7)(8,9)(10,17)(11,15)(12,21)(13,16)(14,19)(18,22)(20,23)Polycyclic presentation:
2^7,3|b^2=e,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10690505, #10690506, #10690508, … |
| maximal normal subgroup of | #10690505, #10690506, #10690508, … |
| maximal quotient of | #10782847, #10782868, #10782870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15861);