Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64845 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #347 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(6,8,10,9,11,18,20,19)(7,12,14,21,16,13,15,17);(2,3,4,5)(6,7,9,13,10,15,18,21,11,16,19,12,20,14,8,17)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=e,d^2=f,e^2=f,b^a=be,d^a=df,g^a=g^2,c^b=cf,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10603832, #10603834, #10603872, … |
| maximal normal subgroup of | #10603832, #10603834, #10603872, … |
| maximal quotient of | #10598515, #10598778, C2×#64890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 228);