Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#359 ⋊ C2 |
| Sylow | C3 ⋊ #2179 |
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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:
(2,3)(4,7,9,22,10,23,26,8)(5,12,14,24,16,13,15,31)(6,18,19,27,21,35,20,25)(11,28,29,17,30,32,33,34);(1,2,3)(4,6)(5,11)(7,18)(8,25)(9,19)(10,21)(12,28)(13,32)(14,29)(15,33)(16,30)(17,24)(20,26)(22,27)(23,35)(31,34);(4,5,9,14,10,16,26,15)(6,17,19,32,21,34,20,28)(7,13,22,31,23,12,8,24)(11,27,29,35,30,25,33,18)Polycyclic presentation:
2^7,3|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2179, C2×#69239, #10948595, … |
| maximal normal subgroup of | D3×#2179, C2×#69239, #10948595, … |
| maximal quotient of | #10706923, #10706929, #10706930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1815);