Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64686 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8)(7,11,12,18)(9,16)(10,15)(13,14,19,20)(17,21);(2,3)(4,5)(6,7)(8,14,15,20)(9,13)(10,12)(11,16,18,21)(17,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,e^2=f,b^a=be,d^a=df,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599490, #10599492, D5×H(3,ℤ/4), … |
| maximal normal subgroup of | #10599490, #10599492, D5×H(3,ℤ/4), … |
| maximal quotient of | #10598105, #10598107, #10598112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 89);