Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#344 ⋊ C2 |
| Sylow | C3 ⋊ #1905 |
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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)(4,7,10,24)(5,12,15,28)(6,17,20,33)(8,23,9,22)(11,25,26,35)(13,21,14,27)(16,30,29,34)(18,32,19,31);(2,3)(4,6)(5,11,15,26)(7,17)(8,18)(9,19)(10,20)(12,25,28,35)(13,16,14,29)(21,30,27,34)(22,31)(23,32)(24,33);(4,5,9,13,10,15,8,14)(6,16,19,26,20,29,18,11)(7,21,23,12,24,27,22,28)(17,25,32,34,33,35,31,30)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^b=eg,h^b=h^2,d^c=dg,e^c=eg,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1905, C2×#69030, #10797081, … |
| maximal normal subgroup of | D3×#1905, C2×#69030, #10797081, … |
| maximal quotient of | #10690604, #10690618, #10690632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1606);