Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2080 |
190 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 59 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)(4,7,8,19,9,20,22,33)(5,11,12,25,13,26,28,35)(6,15,16,31,17,18,21,32)(10,23,14,29,24,34,27,30);(4,6)(5,10)(7,18)(8,21)(9,17)(11,23)(12,27)(13,24)(14,28)(15,20)(16,22)(19,31)(25,30)(26,34)(29,35)(32,33);(2,3)(4,5)(6,14,17,27)(7,11)(8,12)(9,13)(10,16,24,21)(15,30,18,29)(19,25)(20,26)(22,28)(23,32,34,31)(33,35)Polycyclic presentation:
2^7,3|a^2=e,c^2=d,d^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2080, C2×#70294, #10824112, … |
| maximal normal subgroup of | D3×#2080, C2×#70294, #10824112, … |
| maximal quotient of | #10699958, #10699963, #10699968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2870);