Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#484 ⋊ C2 |
| Sylow | C3 ⋊ #3232 |
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 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) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3)(5,11)(9,12)(10,19)(17,18);(2,3)(4,7,8,16)(5,10,11,19)(6,13,14,15)(9,17,12,18)(21,26)(23,31)(25,32)(27,28)(29,35)(33,34);(2,3)(4,6,8,14)(5,9,11,12)(7,15,16,13)(10,18,19,17)(20,22,24,30)(21,25,28,34)(23,29,31,35)(26,32,27,33);(2,3)(4,5)(6,12)(7,10)(8,11)(9,14)(13,18)(15,17)(16,19)(20,21)(22,25)(23,26)(24,28)(27,31)(29,32)(30,34)(33,35)Polycyclic presentation:
2^7,3|b^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^2,c^b=ce,h^b=h^2,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | #10769276, #10769278, #10769285, … |
| maximal normal subgroup of | #10769276, #10769278, #10769285, … |
| maximal quotient of | #10804688, #10804875, #10805714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14038);