Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1833 |
172 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 81 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) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(4,7)(5,11,12,24)(6,15)(8,19)(9,20)(10,22,14,26)(13,18,25,33)(16,29)(17,30)(21,34)(23,32,27,28)(31,35);(2,3)(4,6,8,16,9,17,21,31)(5,10,13,23,12,14,25,27)(7,15,19,29,20,30,34,35)(11,22,18,32,24,26,33,28);(2,3)(4,5)(6,14,17,10)(7,18,20,33)(8,13)(9,12)(11,19,24,34)(15,28)(16,27,31,23)(21,25)(22,29)(26,35)(30,32)Polycyclic presentation:
2^7,3|a^2=f,b^2=e,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg,h^b=h^2,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10711305, #10711306, #10711312, … |
| maximal normal subgroup of | #10711305, #10711306, #10711312, … |
| maximal quotient of | #10688832, #10688836, #10688840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3274);