Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#489 ⋊ C2 |
| Sylow | C3 ⋊ #3239 |
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(2,3)(5,8)(9,10)(13,19)(17,20)(18,27)(25,26);(1,2,3)(5,9)(7,11)(8,10)(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26);(5,8)(9,10)(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25);(4,5)(6,8)(7,9)(10,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,26)(23,25)(24,27)Polycyclic presentation:
2^7,3|b^2=eg,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^d=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | #10776431, #10776435, #10776502, … |
| maximal normal subgroup of | #10776431, #10776435, #10776502, … |
| maximal quotient of | #10804718, #10804923, #10805752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14267);