Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3,5,4)(7,10,11,12)(8,13);(2,3,4,5)(6,7)(8,12,13,10)(9,11)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,b^a=bd,d^a=de,e^a=ef,g^a=g^2,c^b=ce,d^b=df,d^c=df,g^c=g^423 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64864, #10604213, #10604381, … |
| maximal normal subgroup of | C2×#64864, #10604213, #10604381, … |
| maximal quotient of | #10598495, #10598497, #10598499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 202);