Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#117 ⋊ C2 |
| Sylow | C3 ⋊ #2395 |
560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 560 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)(16,18,19,22)(17,21,20,23);(2,3)(5,7)(9,13)(12,15);(4,5)(6,7)(8,10,11,14)(9,12,13,15)(17,20)(21,23);(8,9)(10,12)(11,13)(14,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|b^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10690163, #10690168, #10767340, … |
| maximal normal subgroup of | #10690163, #10690168, #10767340, … |
| maximal quotient of | #10716863, #10716882, #10716897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14850);